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position","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fconfidentialite-position","0.snt-2nde\u002Fse-localisation-cartographie\u002F5.confidentialite-position",{"title":145,"path":146,"stem":147,"children":148},"Informatique embarquée et objets connectés","\u002Fsnt-2nde\u002Fsf-info-embarquee","0.snt-2nde\u002Fsf-info-embarquee\u002F0.index",[149,150,154,158],{"title":145,"path":146,"stem":147},{"title":151,"path":152,"stem":153},"Systèmes informatiques embarqués","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fsystemes-embarques","0.snt-2nde\u002Fsf-info-embarquee\u002F1.systemes-embarques",{"title":155,"path":156,"stem":157},"Capteurs et actionneurs","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fcapteurs-actionneurs","0.snt-2nde\u002Fsf-info-embarquee\u002F2.capteurs-actionneurs",{"title":159,"path":160,"stem":161},"IHM et objets 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Python","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Ftraitement-rgb","0.snt-2nde\u002Fsg-photo-numerique\u002F4.traitement-rgb",{"title":185,"path":186,"stem":187,"children":188},"Notions transversales de programmation","\u002Fsnt-2nde\u002Fsh-prog-notions","0.snt-2nde\u002Fsh-prog-notions\u002F0.index",[189,190,194,198,202],{"title":185,"path":186,"stem":187},{"title":191,"path":192,"stem":193},"Séquences d'instructions et variables","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fsequences-affectations","0.snt-2nde\u002Fsh-prog-notions\u002F1.sequences-affectations",{"title":195,"path":196,"stem":197},"Instructions conditionnelles","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fconditionnelles","0.snt-2nde\u002Fsh-prog-notions\u002F2.conditionnelles",{"title":199,"path":200,"stem":201},"Boucles bornées et non bornées","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Fboucles","0.snt-2nde\u002Fsh-prog-notions\u002F3.boucles",{"title":203,"path":204,"stem":205},"Définitions et appels de fonctions","\u002Fsnt-2nde\u002Fsh-prog-notions\u002Ffonctions","0.snt-2nde\u002Fsh-prog-notions\u002F4.fonctions",{"title":207,"path":208,"stem":209,"children":210},"Démo des widgets MDC","\u002Fsnt-2nde\u002Fzz-demo-widgets","0.snt-2nde\u002Fzz-demo-widgets\u002F0.index",[211,212,216,220],{"title":207,"path":208,"stem":209},{"title":213,"path":214,"stem":215},"Démo statique — callouts, code, BO, illustration","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Fstatique","0.snt-2nde\u002Fzz-demo-widgets\u002F1.statique",{"title":217,"path":218,"stem":219},"Démo interactive — self-eval et python-snippet","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Finteractif","0.snt-2nde\u002Fzz-demo-widgets\u002F2.interactif",{"title":221,"path":222,"stem":223},"Démo · 14 widgets de manipulation NSI","\u002Fsnt-2nde\u002Fzz-demo-widgets\u002Fwidgets-manipulation","0.snt-2nde\u002Fzz-demo-widgets\u002F3.widgets-manipulation",{"title":225,"path":226,"stem":227,"children":228},"NSI — 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deux","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fentiers-relatifs","1.nsi-1ere\u002Fpb-types-valeurs\u002F2.entiers-relatifs",{"title":271,"path":272,"stem":273},"Nombres flottants et virgule flottante","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fflottants","1.nsi-1ere\u002Fpb-types-valeurs\u002F3.flottants",{"title":275,"path":276,"stem":277},"Textes et encodages — ASCII, ISO-8859-1, Unicode","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Ftextes-encodages","1.nsi-1ere\u002Fpb-types-valeurs\u002F4.textes-encodages",{"title":279,"path":280,"stem":281},"Valeurs booléennes et opérateurs logiques","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fbooleens","1.nsi-1ere\u002Fpb-types-valeurs\u002F5.booleens",{"title":283,"path":284,"stem":285,"children":286},"Représentation des données : types construits","\u002Fnsi-1ere\u002Fpc-types-construits","1.nsi-1ere\u002Fpc-types-construits\u002F0.index",[287,288,292,296,300],{"title":283,"path":284,"stem":285},{"title":289,"path":290,"stem":291},"Tableaux et listes","\u002Fnsi-1ere\u002Fpc-types-construits\u002Ftableaux-listes","1.nsi-1ere\u002Fpc-types-construits\u002F1.tableaux-listes",{"title":293,"path":294,"stem":295},"Listes en compréhension","\u002Fnsi-1ere\u002Fpc-types-construits\u002Fcomprehension","1.nsi-1ere\u002Fpc-types-construits\u002F2.comprehension",{"title":297,"path":298,"stem":299},"Tuples et p-uplets nommés","\u002Fnsi-1ere\u002Fpc-types-construits\u002Ftuples","1.nsi-1ere\u002Fpc-types-construits\u002F3.tuples",{"title":301,"path":302,"stem":303},"Dictionnaires","\u002Fnsi-1ere\u002Fpc-types-construits\u002Fdictionnaires","1.nsi-1ere\u002Fpc-types-construits\u002F4.dictionnaires",{"title":305,"path":306,"stem":307,"children":308},"Traitement de données en tables","\u002Fnsi-1ere\u002Fpd-tables-donnees","1.nsi-1ere\u002Fpd-tables-donnees\u002F0.index",[309,310,314,318,322],{"title":305,"path":306,"stem":307},{"title":311,"path":312,"stem":313},"Tables et CSV","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ftables-csv","1.nsi-1ere\u002Fpd-tables-donnees\u002F1.tables-csv",{"title":315,"path":316,"stem":317},"Recherche et filtrage","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Frecherche","1.nsi-1ere\u002Fpd-tables-donnees\u002F2.recherche",{"title":319,"path":320,"stem":321},"Trier une table","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ftri","1.nsi-1ere\u002Fpd-tables-donnees\u002F3.tri",{"title":323,"path":324,"stem":325,"children":326},"Fusion et indexation","\u002Fnsi-1ere\u002Fpd-tables-donnees\u002Ffusion-indexation","1.nsi-1ere\u002Fpd-tables-donnees\u002F4.fusion-indexation",[327],{"title":323,"path":324,"stem":325},{"title":329,"path":330,"stem":331,"children":332},"IHM sur le Web","\u002Fnsi-1ere\u002Fpe-ihm-web","1.nsi-1ere\u002Fpe-ihm-web\u002F0.index",[333,334,338,342,346,350],{"title":329,"path":330,"stem":331},{"title":335,"path":336,"stem":337},"HTML et CSS — rappel de structure","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fhtml-css-bases","1.nsi-1ere\u002Fpe-ihm-web\u002F1.html-css-bases",{"title":339,"path":340,"stem":341},"Formulaires HTML","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fformulaires","1.nsi-1ere\u002Fpe-ihm-web\u002F2.formulaires",{"title":343,"path":344,"stem":345},"Événements JavaScript","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fevenements-js","1.nsi-1ere\u002Fpe-ihm-web\u002F3.evenements-js",{"title":347,"path":348,"stem":349},"Manipulation du DOM","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fdom-interaction","1.nsi-1ere\u002Fpe-ihm-web\u002F4.dom-interaction",{"title":351,"path":352,"stem":353},"Client, serveur et HTTP","\u002Fnsi-1ere\u002Fpe-ihm-web\u002Fclient-serveur-http","1.nsi-1ere\u002Fpe-ihm-web\u002F5.client-serveur-http",{"title":355,"path":356,"stem":357,"children":358},"Architectures matérielles et systèmes d'exploitation","\u002Fnsi-1ere\u002Fpf-archi-os","1.nsi-1ere\u002Fpf-archi-os\u002F0.index",[359,360,364,368,372,376],{"title":355,"path":356,"stem":357},{"title":361,"path":362,"stem":363},"Le modèle de von Neumann","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fvon-neumann","1.nsi-1ere\u002Fpf-archi-os\u002F1.von-neumann",{"title":365,"path":366,"stem":367},"Périphériques et interface homme-machine","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fperipheriques-ihm","1.nsi-1ere\u002Fpf-archi-os\u002F2.peripheriques-ihm",{"title":369,"path":370,"stem":371},"Les systèmes d'exploitation","\u002Fnsi-1ere\u002Fpf-archi-os\u002Fsystemes-exploitation","1.nsi-1ere\u002Fpf-archi-os\u002F3.systemes-exploitation",{"title":373,"path":374,"stem":375},"Linux et le shell","\u002Fnsi-1ere\u002Fpf-archi-os\u002Flinux-shell","1.nsi-1ere\u002Fpf-archi-os\u002F4.linux-shell",{"title":377,"path":378,"stem":379},"Réseaux et protocoles","\u002Fnsi-1ere\u002Fpf-archi-os\u002Freseaux","1.nsi-1ere\u002Fpf-archi-os\u002F5.reseaux",{"title":381,"path":382,"stem":383,"children":384},"Langages et programmation","\u002Fnsi-1ere\u002Fpg-langages-prog","1.nsi-1ere\u002Fpg-langages-prog\u002F0.index",[385,386,390,394,398,402,406],{"title":381,"path":382,"stem":383},{"title":387,"path":388,"stem":389},"Diversité et unité des langages de programmation","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fdiversite-langages","1.nsi-1ere\u002Fpg-langages-prog\u002F1.diversite-langages",{"title":391,"path":392,"stem":393},"Constructions élémentaires","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fconstructions-elementaires","1.nsi-1ere\u002Fpg-langages-prog\u002F2.constructions-elementaires",{"title":395,"path":396,"stem":397},"Fonctions","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Ffonctions","1.nsi-1ere\u002Fpg-langages-prog\u002F3.fonctions",{"title":399,"path":400,"stem":401},"Spécification d'une fonction","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fspecification","1.nsi-1ere\u002Fpg-langages-prog\u002F4.specification",{"title":403,"path":404,"stem":405},"Mise au point des programmes","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fmise-au-point","1.nsi-1ere\u002Fpg-langages-prog\u002F5.mise-au-point",{"title":407,"path":408,"stem":409},"Utilisation de bibliothèques","\u002Fnsi-1ere\u002Fpg-langages-prog\u002Fbibliotheques","1.nsi-1ere\u002Fpg-langages-prog\u002F6.bibliotheques",{"title":411,"path":412,"stem":413,"children":414},"Algorithmique","\u002Fnsi-1ere\u002Fph-algorithmique","1.nsi-1ere\u002Fph-algorithmique\u002F0.index",[415,416,420,424,428,432,436],{"title":411,"path":412,"stem":413},{"title":417,"path":418,"stem":419},"Parcours séquentiel d'un tableau","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fparcours-sequentiel","1.nsi-1ere\u002Fph-algorithmique\u002F1.parcours-sequentiel",{"title":421,"path":422,"stem":423},"Bases de la complexité","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fcomplexite-bases","1.nsi-1ere\u002Fph-algorithmique\u002F2.complexite-bases",{"title":425,"path":426,"stem":427},"Tris par sélection et par insertion","\u002Fnsi-1ere\u002Fph-algorithmique\u002Ftris","1.nsi-1ere\u002Fph-algorithmique\u002F3.tris",{"title":429,"path":430,"stem":431},"Recherche dichotomique","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fdichotomie","1.nsi-1ere\u002Fph-algorithmique\u002F4.dichotomie",{"title":433,"path":434,"stem":435},"Algorithmes gloutons","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fgloutons","1.nsi-1ere\u002Fph-algorithmique\u002F5.gloutons",{"title":437,"path":438,"stem":439},"Les k plus proches voisins (k-NN)","\u002Fnsi-1ere\u002Fph-algorithmique\u002Fknn","1.nsi-1ere\u002Fph-algorithmique\u002F6.knn",{"title":441,"path":442,"stem":443,"children":444},"NSI — Terminale","\u002Fnsi-tale","2.nsi-tale\u002F0.index",[445,446,450,476,498,536,560],{"title":441,"path":442,"stem":443},{"title":447,"path":448,"stem":449},"Review pédagogique — chapitres NSI Terminale (TA, TB, TC, TD, TE)","\u002Fnsi-tale\u002Freview","2.nsi-tale\u002FREVIEW",{"title":451,"path":452,"stem":453,"children":454},"Structures de données","\u002Fnsi-tale\u002Fta-structures-donnees","2.nsi-tale\u002Fta-structures-donnees\u002F0.index",[455,456,460,464,468,472],{"title":451,"path":452,"stem":453},{"title":457,"path":458,"stem":459},"Objet, classe, interface","\u002Fnsi-tale\u002Fta-structures-donnees\u002Finterface-implementation","2.nsi-tale\u002Fta-structures-donnees\u002F1.interface-implementation",{"title":461,"path":462,"stem":463},"Implémenter une structure — l'exemple de la file FIFO","\u002Fnsi-tale\u002Fta-structures-donnees\u002Fimplementer-une-structure","2.nsi-tale\u002Fta-structures-donnees\u002F2.implementer-une-structure",{"title":465,"path":466,"stem":467},"Listes, piles, files, dictionnaires","\u002Fnsi-tale\u002Fta-structures-donnees\u002Flistes-piles-files-dict","2.nsi-tale\u002Fta-structures-donnees\u002F3.listes-piles-files-dict",{"title":469,"path":470,"stem":471},"Arbres binaires","\u002Fnsi-tale\u002Fta-structures-donnees\u002Farbres-binaires","2.nsi-tale\u002Fta-structures-donnees\u002F4.arbres-binaires",{"title":473,"path":474,"stem":475},"Graphes","\u002Fnsi-tale\u002Fta-structures-donnees\u002Fgraphes","2.nsi-tale\u002Fta-structures-donnees\u002F5.graphes",{"title":477,"path":478,"stem":479,"children":480},"Bases de données","\u002Fnsi-tale\u002Ftb-bases-de-donnees","2.nsi-tale\u002Ftb-bases-de-donnees\u002F0.index",[481,482,486,490,494],{"title":477,"path":478,"stem":479},{"title":483,"path":484,"stem":485},"Le modèle relationnel","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fmodele-relationnel","2.nsi-tale\u002Ftb-bases-de-donnees\u002F1.modele-relationnel",{"title":487,"path":488,"stem":489},"Bases de données relationnelles et anomalies de schéma","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fbase-relationnelle","2.nsi-tale\u002Ftb-bases-de-donnees\u002F2.base-relationnelle",{"title":491,"path":492,"stem":493},"Le langage SQL","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fsql","2.nsi-tale\u002Ftb-bases-de-donnees\u002F3.sql",{"title":495,"path":496,"stem":497},"Les systèmes de gestion de bases de données","\u002Fnsi-tale\u002Ftb-bases-de-donnees\u002Fsgbd","2.nsi-tale\u002Ftb-bases-de-donnees\u002F4.sgbd",{"title":499,"path":500,"stem":501,"children":502},"Architectures matérielles, systèmes d'exploitation et réseaux","\u002Fnsi-tale\u002Ftc-archi-os-reseaux","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F0.index",[503,504,508,512,516,520,524,528,532],{"title":499,"path":500,"stem":501},{"title":505,"path":506,"stem":507},"Le système sur puce (SoC)","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fsysteme-sur-puce","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F1.systeme-sur-puce",{"title":509,"path":510,"stem":511},"Processus et ordonnancement par l'OS","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fprocessus-os","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F2.processus-os",{"title":513,"path":514,"stem":515},"L'interblocage (deadlock)","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Finterblocage","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F3.interblocage",{"title":517,"path":518,"stem":519},"Principes du routage","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Froutage-principes","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F4.routage-principes",{"title":521,"path":522,"stem":523},"Protocoles de routage RIP et OSPF","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fprotocoles-rip-ospf","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F5.protocoles-rip-ospf",{"title":525,"path":526,"stem":527},"Chiffrement symétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fchiffrement-symetrique","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F6.chiffrement-symetrique",{"title":529,"path":530,"stem":531},"Chiffrement asymétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fchiffrement-asymetrique","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F7.chiffrement-asymetrique",{"title":533,"path":534,"stem":535},"HTTPS — l'échange de clé symétrique","\u002Fnsi-tale\u002Ftc-archi-os-reseaux\u002Fhttps-tls","2.nsi-tale\u002Ftc-archi-os-reseaux\u002F8.https-tls",{"title":381,"path":537,"stem":538,"children":539},"\u002Fnsi-tale\u002Ftd-langages-prog","2.nsi-tale\u002Ftd-langages-prog\u002F0.index",[540,541,544,548,552,556],{"title":381,"path":537,"stem":538},{"title":403,"path":542,"stem":543},"\u002Fnsi-tale\u002Ftd-langages-prog\u002Fmise-au-point","2.nsi-tale\u002Ftd-langages-prog\u002F1.mise-au-point",{"title":545,"path":546,"stem":547},"Modularité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fmodularite","2.nsi-tale\u002Ftd-langages-prog\u002F2.modularite",{"title":549,"path":550,"stem":551},"Récursivité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Frecursivite","2.nsi-tale\u002Ftd-langages-prog\u002F3.recursivite",{"title":553,"path":554,"stem":555},"Paradigmes de programmation","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fparadigmes","2.nsi-tale\u002Ftd-langages-prog\u002F4.paradigmes",{"title":557,"path":558,"stem":559},"Programme comme donnée — calculabilité et indécidabilité","\u002Fnsi-tale\u002Ftd-langages-prog\u002Fprogramme-comme-donnee","2.nsi-tale\u002Ftd-langages-prog\u002F5.programme-comme-donnee",{"title":411,"path":561,"stem":562,"children":563},"\u002Fnsi-tale\u002Fte-algorithmique","2.nsi-tale\u002Fte-algorithmique\u002F0.index",[564,565,569,573,577,581],{"title":411,"path":561,"stem":562},{"title":566,"path":567,"stem":568},"Algorithmes sur les arbres binaires","\u002Fnsi-tale\u002Fte-algorithmique\u002Farbres-binaires-algos","2.nsi-tale\u002Fte-algorithmique\u002F1.arbres-binaires-algos",{"title":570,"path":571,"stem":572},"Parcours de graphes — DFS, BFS, cycles, chemins","\u002Fnsi-tale\u002Fte-algorithmique\u002Fgraphes-parcours","2.nsi-tale\u002Fte-algorithmique\u002F2.graphes-parcours",{"title":574,"path":575,"stem":576},"Diviser pour régner","\u002Fnsi-tale\u002Fte-algorithmique\u002Fdiviser-pour-regner","2.nsi-tale\u002Fte-algorithmique\u002F3.diviser-pour-regner",{"title":578,"path":579,"stem":580},"Programmation dynamique","\u002Fnsi-tale\u002Fte-algorithmique\u002Fprogrammation-dynamique","2.nsi-tale\u002Fte-algorithmique\u002F4.programmation-dynamique",{"title":582,"path":583,"stem":584},"Recherche textuelle — l'algorithme de Boyer-Moore","\u002Fnsi-tale\u002Fte-algorithmique\u002Frecherche-textuelle","2.nsi-tale\u002Fte-algorithmique\u002F5.recherche-textuelle",{"id":586,"title":263,"bo":587,"body":589,"description":5634,"eval":5635,"extension":5636,"labo":5635,"meta":5637,"navigation":5638,"path":264,"quizzes":5639,"readingTime":2888,"seo":5648,"stem":265,"tp":5635,"__hash__":5649},"cours\u002F1.nsi-1ere\u002Fpb-types-valeurs\u002F1.bases-entiers-positifs.md",[588],"PB01",{"type":590,"value":591,"toc":5623},"minimark",[592,597,831,858,894,1132,1592,1857,1966,2097,2282,2286,2293,2375,2869,2876,2964,3072,3076,3087,3118,3601,3706,3822,3825,3833,3837,3844,4025,4225,4232,4341,4345,4549,5111,5279,5336,5340,5545,5549,5619],[593,594,596],"h2",{"id":595},"introduction","Introduction",[598,599,600,601,605,606,699,700,762,763,826,827,830],"p",{},"Quand vous écrivez ",[602,603,604],"strong",{},"2026",", vous utilisez sans y penser une convention :\nchaque chiffre occupe une position qui correspond à une puissance de 10. La\nposition des unités vaut ",[607,608,611,640],"span",{"className":609},[610],"katex",[607,612,615],{"className":613},[614],"katex-mathml",[616,617,619],"math",{"xmlns":618},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[620,621,622,635],"semantics",{},[623,624,625],"mrow",{},[626,627,628,632],"msup",{},[629,630,631],"mn",{},"10",[629,633,634],{},"0",[636,637,639],"annotation",{"encoding":638},"application\u002Fx-tex","10^0",[607,641,645],{"className":642,"ariaHidden":644},[643],"katex-html","true",[607,646,649,654,659],{"className":647},[648],"base",[607,650],{"className":651,"style":653},[652],"strut","height:0.8141em;",[607,655,658],{"className":656},[657],"mord","1",[607,660,662,665],{"className":661},[657],[607,663,634],{"className":664},[657],[607,666,669],{"className":667},[668],"msupsub",[607,670,673],{"className":671},[672],"vlist-t",[607,674,677],{"className":675},[676],"vlist-r",[607,678,681],{"className":679,"style":653},[680],"vlist",[607,682,684,689],{"style":683},"top:-3.063em;margin-right:0.05em;",[607,685],{"className":686,"style":688},[687],"pstrut","height:2.7em;",[607,690,696],{"className":691},[692,693,694,695],"sizing","reset-size6","size3","mtight",[607,697,634],{"className":698},[657,695],", celle des dizaines ",[607,701,703,721],{"className":702},[610],[607,704,706],{"className":705},[614],[616,707,708],{"xmlns":618},[620,709,710,718],{},[623,711,712],{},[626,713,714,716],{},[629,715,631],{},[629,717,658],{},[636,719,720],{"encoding":638},"10^1",[607,722,724],{"className":723,"ariaHidden":644},[643],[607,725,727,730,733],{"className":726},[648],[607,728],{"className":729,"style":653},[652],[607,731,658],{"className":732},[657],[607,734,736,739],{"className":735},[657],[607,737,634],{"className":738},[657],[607,740,742],{"className":741},[668],[607,743,745],{"className":744},[672],[607,746,748],{"className":747},[676],[607,749,751],{"className":750,"style":653},[680],[607,752,753,756],{"style":683},[607,754],{"className":755,"style":688},[687],[607,757,759],{"className":758},[692,693,694,695],[607,760,658],{"className":761},[657,695],", celle des centaines\n",[607,764,766,785],{"className":765},[610],[607,767,769],{"className":768},[614],[616,770,771],{"xmlns":618},[620,772,773,782],{},[623,774,775],{},[626,776,777,779],{},[629,778,631],{},[629,780,781],{},"2",[636,783,784],{"encoding":638},"10^2",[607,786,788],{"className":787,"ariaHidden":644},[643],[607,789,791,794,797],{"className":790},[648],[607,792],{"className":793,"style":653},[652],[607,795,658],{"className":796},[657],[607,798,800,803],{"className":799},[657],[607,801,634],{"className":802},[657],[607,804,806],{"className":805},[668],[607,807,809],{"className":808},[672],[607,810,812],{"className":811},[676],[607,813,815],{"className":814,"style":653},[680],[607,816,817,820],{"style":683},[607,818],{"className":819,"style":688},[687],[607,821,823],{"className":822},[692,693,694,695],[607,824,781],{"className":825},[657,695],", et ainsi de suite. C'est la ",[602,828,829],{},"base 10",", ou notation décimale.",[598,832,833,834,837,838,841,842,846,847,850,851,854,855],{},"Un ordinateur, lui, ne distingue physiquement que deux états : courant qui\npasse ou non, aimantation positive ou négative, tension haute ou basse. Il est\ndonc naturel qu'il travaille en ",[602,835,836],{},"base 2"," : il n'utilise que deux chiffres, 0\net 1, appelés ",[602,839,840],{},"bits"," (",[843,844,845],"em",{},"binary digit","). Pour faciliter la lecture humaine de\nces longues suites de bits, on utilise aussi la ",[602,848,849],{},"base 16"," (hexadécimal) et,\nplus rarement, la ",[602,852,853],{},"base 8"," (octal). ",[856,857],"bo-ref",{"code":588},[593,859,861,862],{"id":860},"le-principe-dune-base-bbb","Le principe d'une base ",[607,863,865,880],{"className":864},[610],[607,866,868],{"className":867},[614],[616,869,870],{"xmlns":618},[620,871,872,878],{},[623,873,874],{},[875,876,877],"mi",{},"b",[636,879,877],{"encoding":638},[607,881,883],{"className":882,"ariaHidden":644},[643],[607,884,886,890],{"className":885},[648],[607,887],{"className":888,"style":889},[652],"height:0.6944em;",[607,891,877],{"className":892},[657,893],"mathnormal",[598,895,896,897,925,926,984,985,1013,1014,1042,1043,1098,1099,1102,1103,1131],{},"Dans une base ",[607,898,900,913],{"className":899},[610],[607,901,903],{"className":902},[614],[616,904,905],{"xmlns":618},[620,906,907,911],{},[623,908,909],{},[875,910,877],{},[636,912,877],{"encoding":638},[607,914,916],{"className":915,"ariaHidden":644},[643],[607,917,919,922],{"className":918},[648],[607,920],{"className":921,"style":889},[652],[607,923,877],{"className":924},[657,893]," (avec ",[607,927,929,949],{"className":928},[610],[607,930,932],{"className":931},[614],[616,933,934],{"xmlns":618},[620,935,936,946],{},[623,937,938,940,944],{},[875,939,877],{},[941,942,943],"mo",{},"≥",[629,945,781],{},[636,947,948],{"encoding":638},"b \\geq 2",[607,950,952,974],{"className":951,"ariaHidden":644},[643],[607,953,955,959,962,967,971],{"className":954},[648],[607,956],{"className":957,"style":958},[652],"height:0.8304em;vertical-align:-0.136em;",[607,960,877],{"className":961},[657,893],[607,963],{"className":964,"style":966},[965],"mspace","margin-right:0.2778em;",[607,968,943],{"className":969},[970],"mrel",[607,972],{"className":973,"style":966},[965],[607,975,977,981],{"className":976},[648],[607,978],{"className":979,"style":980},[652],"height:0.6444em;",[607,982,781],{"className":983},[657],"), on dispose de ",[607,986,988,1001],{"className":987},[610],[607,989,991],{"className":990},[614],[616,992,993],{"xmlns":618},[620,994,995,999],{},[623,996,997],{},[875,998,877],{},[636,1000,877],{"encoding":638},[607,1002,1004],{"className":1003,"ariaHidden":644},[643],[607,1005,1007,1010],{"className":1006},[648],[607,1008],{"className":1009,"style":889},[652],[607,1011,877],{"className":1012},[657,893]," chiffres distincts, allant\nde ",[607,1015,1017,1030],{"className":1016},[610],[607,1018,1020],{"className":1019},[614],[616,1021,1022],{"xmlns":618},[620,1023,1024,1028],{},[623,1025,1026],{},[629,1027,634],{},[636,1029,634],{"encoding":638},[607,1031,1033],{"className":1032,"ariaHidden":644},[643],[607,1034,1036,1039],{"className":1035},[648],[607,1037],{"className":1038,"style":980},[652],[607,1040,634],{"className":1041},[657]," à ",[607,1044,1046,1065],{"className":1045},[610],[607,1047,1049],{"className":1048},[614],[616,1050,1051],{"xmlns":618},[620,1052,1053,1062],{},[623,1054,1055,1057,1060],{},[875,1056,877],{},[941,1058,1059],{},"−",[629,1061,658],{},[636,1063,1064],{"encoding":638},"b-1",[607,1066,1068,1089],{"className":1067,"ariaHidden":644},[643],[607,1069,1071,1075,1078,1082,1086],{"className":1070},[648],[607,1072],{"className":1073,"style":1074},[652],"height:0.7778em;vertical-align:-0.0833em;",[607,1076,877],{"className":1077},[657,893],[607,1079],{"className":1080,"style":1081},[965],"margin-right:0.2222em;",[607,1083,1059],{"className":1084},[1085],"mbin",[607,1087],{"className":1088,"style":1081},[965],[607,1090,1092,1095],{"className":1091},[648],[607,1093],{"className":1094,"style":980},[652],[607,1096,658],{"className":1097},[657],". Un nombre s'écrit comme une suite de ces chiffres, et la\n",[602,1100,1101],{},"valeur"," du nombre se calcule en sommant chaque chiffre multiplié par la\npuissance de ",[607,1104,1106,1119],{"className":1105},[610],[607,1107,1109],{"className":1108},[614],[616,1110,1111],{"xmlns":618},[620,1112,1113,1117],{},[623,1114,1115],{},[875,1116,877],{},[636,1118,877],{"encoding":638},[607,1120,1122],{"className":1121,"ariaHidden":644},[643],[607,1123,1125,1128],{"className":1124},[648],[607,1126],{"className":1127,"style":889},[652],[607,1129,877],{"className":1130},[657,893]," correspondant à sa position.",[598,1133,1134,1135,1455,1456,1484,1485,1558,1559,1562,1563,1591],{},"Pour un nombre noté ",[607,1136,1138,1203],{"className":1137},[610],[607,1139,1141],{"className":1140},[614],[616,1142,1143],{"xmlns":618},[620,1144,1145,1200],{},[623,1146,1147,1151,1166,1178,1181,1187,1193],{},[941,1148,1150],{"stretchy":1149},"false","(",[1152,1153,1154,1157],"msub",{},[875,1155,1156],{},"c",[623,1158,1159,1162,1164],{},[875,1160,1161],{},"n",[941,1163,1059],{},[629,1165,658],{},[1152,1167,1168,1170],{},[875,1169,1156],{},[623,1171,1172,1174,1176],{},[875,1173,1161],{},[941,1175,1059],{},[629,1177,781],{},[941,1179,1180],{},"…",[1152,1182,1183,1185],{},[875,1184,1156],{},[629,1186,658],{},[1152,1188,1189,1191],{},[875,1190,1156],{},[629,1192,634],{},[1152,1194,1195,1198],{},[941,1196,1197],{"stretchy":1149},")",[875,1199,877],{},[636,1201,1202],{"encoding":638},"(c_{n-1} c_{n-2} \\ldots c_1 c_0)_b",[607,1204,1206],{"className":1205,"ariaHidden":644},[643],[607,1207,1209,1213,1217,1272,1321,1325,1329,1332,1373,1413],{"className":1208},[648],[607,1210],{"className":1211,"style":1212},[652],"height:1em;vertical-align:-0.25em;",[607,1214,1150],{"className":1215},[1216],"mopen",[607,1218,1220,1223],{"className":1219},[657],[607,1221,1156],{"className":1222},[657,893],[607,1224,1226],{"className":1225},[668],[607,1227,1230,1263],{"className":1228},[672,1229],"vlist-t2",[607,1231,1233,1258],{"className":1232},[676],[607,1234,1237],{"className":1235,"style":1236},[680],"height:0.3011em;",[607,1238,1240,1243],{"style":1239},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[607,1241],{"className":1242,"style":688},[687],[607,1244,1246],{"className":1245},[692,693,694,695],[607,1247,1249,1252,1255],{"className":1248},[657,695],[607,1250,1161],{"className":1251},[657,893,695],[607,1253,1059],{"className":1254},[1085,695],[607,1256,658],{"className":1257},[657,695],[607,1259,1262],{"className":1260},[1261],"vlist-s","​",[607,1264,1266],{"className":1265},[676],[607,1267,1270],{"className":1268,"style":1269},[680],"height:0.2083em;",[607,1271],{},[607,1273,1275,1278],{"className":1274},[657],[607,1276,1156],{"className":1277},[657,893],[607,1279,1281],{"className":1280},[668],[607,1282,1284,1313],{"className":1283},[672,1229],[607,1285,1287,1310],{"className":1286},[676],[607,1288,1290],{"className":1289,"style":1236},[680],[607,1291,1292,1295],{"style":1239},[607,1293],{"className":1294,"style":688},[687],[607,1296,1298],{"className":1297},[692,693,694,695],[607,1299,1301,1304,1307],{"className":1300},[657,695],[607,1302,1161],{"className":1303},[657,893,695],[607,1305,1059],{"className":1306},[1085,695],[607,1308,781],{"className":1309},[657,695],[607,1311,1262],{"className":1312},[1261],[607,1314,1316],{"className":1315},[676],[607,1317,1319],{"className":1318,"style":1269},[680],[607,1320],{},[607,1322],{"className":1323,"style":1324},[965],"margin-right:0.1667em;",[607,1326,1180],{"className":1327},[1328],"minner",[607,1330],{"className":1331,"style":1324},[965],[607,1333,1335,1338],{"className":1334},[657],[607,1336,1156],{"className":1337},[657,893],[607,1339,1341],{"className":1340},[668],[607,1342,1344,1364],{"className":1343},[672,1229],[607,1345,1347,1361],{"className":1346},[676],[607,1348,1350],{"className":1349,"style":1236},[680],[607,1351,1352,1355],{"style":1239},[607,1353],{"className":1354,"style":688},[687],[607,1356,1358],{"className":1357},[692,693,694,695],[607,1359,658],{"className":1360},[657,695],[607,1362,1262],{"className":1363},[1261],[607,1365,1367],{"className":1366},[676],[607,1368,1371],{"className":1369,"style":1370},[680],"height:0.15em;",[607,1372],{},[607,1374,1376,1379],{"className":1375},[657],[607,1377,1156],{"className":1378},[657,893],[607,1380,1382],{"className":1381},[668],[607,1383,1385,1405],{"className":1384},[672,1229],[607,1386,1388,1402],{"className":1387},[676],[607,1389,1391],{"className":1390,"style":1236},[680],[607,1392,1393,1396],{"style":1239},[607,1394],{"className":1395,"style":688},[687],[607,1397,1399],{"className":1398},[692,693,694,695],[607,1400,634],{"className":1401},[657,695],[607,1403,1262],{"className":1404},[1261],[607,1406,1408],{"className":1407},[676],[607,1409,1411],{"className":1410,"style":1370},[680],[607,1412],{},[607,1414,1417,1420],{"className":1415},[1416],"mclose",[607,1418,1197],{"className":1419},[1416],[607,1421,1423],{"className":1422},[668],[607,1424,1426,1447],{"className":1425},[672,1229],[607,1427,1429,1444],{"className":1428},[676],[607,1430,1433],{"className":1431,"style":1432},[680],"height:0.3361em;",[607,1434,1435,1438],{"style":1239},[607,1436],{"className":1437,"style":688},[687],[607,1439,1441],{"className":1440},[692,693,694,695],[607,1442,877],{"className":1443},[657,893,695],[607,1445,1262],{"className":1446},[1261],[607,1448,1450],{"className":1449},[676],[607,1451,1453],{"className":1452,"style":1370},[680],[607,1454],{}," dans la base ",[607,1457,1459,1472],{"className":1458},[610],[607,1460,1462],{"className":1461},[614],[616,1463,1464],{"xmlns":618},[620,1465,1466,1470],{},[623,1467,1468],{},[875,1469,877],{},[636,1471,877],{"encoding":638},[607,1473,1475],{"className":1474,"ariaHidden":644},[643],[607,1476,1478,1481],{"className":1477},[648],[607,1479],{"className":1480,"style":889},[652],[607,1482,877],{"className":1483},[657,893],"\n(les ",[607,1486,1488,1507],{"className":1487},[610],[607,1489,1491],{"className":1490},[614],[616,1492,1493],{"xmlns":618},[620,1494,1495,1504],{},[623,1496,1497],{},[1152,1498,1499,1501],{},[875,1500,1156],{},[875,1502,1503],{},"i",[636,1505,1506],{"encoding":638},"c_i",[607,1508,1510],{"className":1509,"ariaHidden":644},[643],[607,1511,1513,1517],{"className":1512},[648],[607,1514],{"className":1515,"style":1516},[652],"height:0.5806em;vertical-align:-0.15em;",[607,1518,1520,1523],{"className":1519},[657],[607,1521,1156],{"className":1522},[657,893],[607,1524,1526],{"className":1525},[668],[607,1527,1529,1550],{"className":1528},[672,1229],[607,1530,1532,1547],{"className":1531},[676],[607,1533,1536],{"className":1534,"style":1535},[680],"height:0.3117em;",[607,1537,1538,1541],{"style":1239},[607,1539],{"className":1540,"style":688},[687],[607,1542,1544],{"className":1543},[692,693,694,695],[607,1545,1503],{"className":1546},[657,893,695],[607,1548,1262],{"className":1549},[1261],[607,1551,1553],{"className":1552},[676],[607,1554,1556],{"className":1555,"style":1370},[680],[607,1557],{}," étant les ",[602,1560,1561],{},"chiffres",", à ne pas confondre avec la base ",[607,1564,1566,1579],{"className":1565},[610],[607,1567,1569],{"className":1568},[614],[616,1570,1571],{"xmlns":618},[620,1572,1573,1577],{},[623,1574,1575],{},[875,1576,877],{},[636,1578,877],{"encoding":638},[607,1580,1582],{"className":1581,"ariaHidden":644},[643],[607,1583,1585,1588],{"className":1584},[648],[607,1586],{"className":1587,"style":889},[652],[607,1589,877],{"className":1590},[657,893],") :",[607,1593,1596],{"className":1594},[1595],"katex-display",[607,1597,1599,1655],{"className":1598},[610],[607,1600,1602],{"className":1601},[614],[616,1603,1605],{"xmlns":618,"display":1604},"block",[620,1606,1607,1652],{},[623,1608,1609,1612,1615,1637,1643,1646],{},[875,1610,1611],{},"N",[941,1613,1614],{},"=",[1616,1617,1618,1621,1629],"munderover",{},[941,1619,1620],{},"∑",[623,1622,1623,1625,1627],{},[875,1624,1503],{},[941,1626,1614],{},[629,1628,634],{},[623,1630,1631,1633,1635],{},[875,1632,1161],{},[941,1634,1059],{},[629,1636,658],{},[1152,1638,1639,1641],{},[875,1640,1156],{},[875,1642,1503],{},[941,1644,1645],{},"⋅",[626,1647,1648,1650],{},[875,1649,877],{},[875,1651,1503],{},[636,1653,1654],{"encoding":638},"N = \\sum_{i=0}^{n-1} c_i \\cdot b^i",[607,1656,1658,1678,1820],{"className":1657,"ariaHidden":644},[643],[607,1659,1661,1665,1669,1672,1675],{"className":1660},[648],[607,1662],{"className":1663,"style":1664},[652],"height:0.6833em;",[607,1666,1611],{"className":1667,"style":1668},[657,893],"margin-right:0.109em;",[607,1670],{"className":1671,"style":966},[965],[607,1673,1614],{"className":1674},[970],[607,1676],{"className":1677,"style":966},[965],[607,1679,1681,1685,1768,1771,1811,1814,1817],{"className":1680},[648],[607,1682],{"className":1683,"style":1684},[652],"height:3.0788em;vertical-align:-1.2777em;",[607,1686,1690],{"className":1687},[1688,1689],"mop","op-limits",[607,1691,1693,1759],{"className":1692},[672,1229],[607,1694,1696,1756],{"className":1695},[676],[607,1697,1700,1722,1735],{"className":1698,"style":1699},[680],"height:1.8011em;",[607,1701,1703,1707],{"style":1702},"top:-1.8723em;margin-left:0em;",[607,1704],{"className":1705,"style":1706},[687],"height:3.05em;",[607,1708,1710],{"className":1709},[692,693,694,695],[607,1711,1713,1716,1719],{"className":1712},[657,695],[607,1714,1503],{"className":1715},[657,893,695],[607,1717,1614],{"className":1718},[970,695],[607,1720,634],{"className":1721},[657,695],[607,1723,1725,1728],{"style":1724},"top:-3.05em;",[607,1726],{"className":1727,"style":1706},[687],[607,1729,1730],{},[607,1731,1620],{"className":1732},[1688,1733,1734],"op-symbol","large-op",[607,1736,1738,1741],{"style":1737},"top:-4.3em;margin-left:0em;",[607,1739],{"className":1740,"style":1706},[687],[607,1742,1744],{"className":1743},[692,693,694,695],[607,1745,1747,1750,1753],{"className":1746},[657,695],[607,1748,1161],{"className":1749},[657,893,695],[607,1751,1059],{"className":1752},[1085,695],[607,1754,658],{"className":1755},[657,695],[607,1757,1262],{"className":1758},[1261],[607,1760,1762],{"className":1761},[676],[607,1763,1766],{"className":1764,"style":1765},[680],"height:1.2777em;",[607,1767],{},[607,1769],{"className":1770,"style":1324},[965],[607,1772,1774,1777],{"className":1773},[657],[607,1775,1156],{"className":1776},[657,893],[607,1778,1780],{"className":1779},[668],[607,1781,1783,1803],{"className":1782},[672,1229],[607,1784,1786,1800],{"className":1785},[676],[607,1787,1789],{"className":1788,"style":1535},[680],[607,1790,1791,1794],{"style":1239},[607,1792],{"className":1793,"style":688},[687],[607,1795,1797],{"className":1796},[692,693,694,695],[607,1798,1503],{"className":1799},[657,893,695],[607,1801,1262],{"className":1802},[1261],[607,1804,1806],{"className":1805},[676],[607,1807,1809],{"className":1808,"style":1370},[680],[607,1810],{},[607,1812],{"className":1813,"style":1081},[965],[607,1815,1645],{"className":1816},[1085],[607,1818],{"className":1819,"style":1081},[965],[607,1821,1823,1827],{"className":1822},[648],[607,1824],{"className":1825,"style":1826},[652],"height:0.8747em;",[607,1828,1830,1833],{"className":1829},[657],[607,1831,877],{"className":1832},[657,893],[607,1834,1836],{"className":1835},[668],[607,1837,1839],{"className":1838},[672],[607,1840,1842],{"className":1841},[676],[607,1843,1845],{"className":1844,"style":1826},[680],[607,1846,1848,1851],{"style":1847},"top:-3.113em;margin-right:0.05em;",[607,1849],{"className":1850,"style":688},[687],[607,1852,1854],{"className":1853},[692,693,694,695],[607,1855,1503],{"className":1856},[657,893,695],[1858,1859,1860,1879],"table",{},[1861,1862,1863],"thead",{},[1864,1865,1866,1870,1873,1876],"tr",{},[1867,1868,1869],"th",{},"Base",[1867,1871,1872],{},"Nom",[1867,1874,1875],{},"Chiffres utilisés",[1867,1877,1878],{},"Préfixe Python",[1880,1881,1882,1903,1923,1940],"tbody",{},[1864,1883,1884,1887,1890,1898],{},[1885,1886,781],"td",{},[1885,1888,1889],{},"binaire",[1885,1891,1892,1895,1896],{},[1893,1894,634],"code",{},", ",[1893,1897,658],{},[1885,1899,1900],{},[1893,1901,1902],{},"0b",[1864,1904,1905,1908,1911,1918],{},[1885,1906,1907],{},"8",[1885,1909,1910],{},"octal",[1885,1912,1913,1042,1915],{},[1893,1914,634],{},[1893,1916,1917],{},"7",[1885,1919,1920],{},[1893,1921,1922],{},"0o",[1864,1924,1925,1927,1930,1937],{},[1885,1926,631],{},[1885,1928,1929],{},"décimal",[1885,1931,1932,1042,1934],{},[1893,1933,634],{},[1893,1935,1936],{},"9",[1885,1938,1939],{},"aucun",[1864,1941,1942,1945,1948,1961],{},[1885,1943,1944],{},"16",[1885,1946,1947],{},"hexadécimal",[1885,1949,1950,1042,1952,1954,1955,1042,1958],{},[1893,1951,634],{},[1893,1953,1936],{},", puis ",[1893,1956,1957],{},"A",[1893,1959,1960],{},"F",[1885,1962,1963],{},[1893,1964,1965],{},"0x",[598,1967,1968,1969,1042,1971,1973,1974,1042,2002,2031,2032,2035,2036,2065,2066,2035,2068,2096],{},"En hexadécimal, les lettres ",[1893,1970,1957],{},[1893,1972,1960],{}," représentent les valeurs ",[607,1975,1977,1990],{"className":1976},[610],[607,1978,1980],{"className":1979},[614],[616,1981,1982],{"xmlns":618},[620,1983,1984,1988],{},[623,1985,1986],{},[629,1987,631],{},[636,1989,631],{"encoding":638},[607,1991,1993],{"className":1992,"ariaHidden":644},[643],[607,1994,1996,1999],{"className":1995},[648],[607,1997],{"className":1998,"style":980},[652],[607,2000,631],{"className":2001},[657],[607,2003,2005,2019],{"className":2004},[610],[607,2006,2008],{"className":2007},[614],[616,2009,2010],{"xmlns":618},[620,2011,2012,2017],{},[623,2013,2014],{},[629,2015,2016],{},"15",[636,2018,2016],{"encoding":638},[607,2020,2022],{"className":2021,"ariaHidden":644},[643],[607,2023,2025,2028],{"className":2024},[648],[607,2026],{"className":2027,"style":980},[652],[607,2029,2016],{"className":2030},[657],".\nAinsi, ",[1893,2033,2034],{},"B"," vaut ",[607,2037,2039,2053],{"className":2038},[610],[607,2040,2042],{"className":2041},[614],[616,2043,2044],{"xmlns":618},[620,2045,2046,2051],{},[623,2047,2048],{},[629,2049,2050],{},"11",[636,2052,2050],{"encoding":638},[607,2054,2056],{"className":2055,"ariaHidden":644},[643],[607,2057,2059,2062],{"className":2058},[648],[607,2060],{"className":2061,"style":980},[652],[607,2063,2050],{"className":2064},[657]," et ",[1893,2067,1960],{},[607,2069,2071,2084],{"className":2070},[610],[607,2072,2074],{"className":2073},[614],[616,2075,2076],{"xmlns":618},[620,2077,2078,2082],{},[623,2079,2080],{},[629,2081,2016],{},[636,2083,2016],{"encoding":638},[607,2085,2087],{"className":2086,"ariaHidden":644},[643],[607,2088,2090,2093],{"className":2089},[648],[607,2091],{"className":2092,"style":980},[652],[607,2094,2016],{"className":2095},[657],".",[2098,2099,2100],"note",{},[598,2101,2102,2103,2184,2185,2274,2275,1895,2277,2065,2279,2281],{},"Pour lever toute ambiguïté, on note souvent la base en indice :\n",[607,2104,2106,2129],{"className":2105},[610],[607,2107,2109],{"className":2108},[614],[616,2110,2111],{"xmlns":618},[620,2112,2113,2126],{},[623,2114,2115,2117,2120],{},[941,2116,1150],{"stretchy":1149},[629,2118,2119],{},"1011",[1152,2121,2122,2124],{},[941,2123,1197],{"stretchy":1149},[629,2125,781],{},[636,2127,2128],{"encoding":638},"(1011)_2",[607,2130,2132],{"className":2131,"ariaHidden":644},[643],[607,2133,2135,2138,2141,2144],{"className":2134},[648],[607,2136],{"className":2137,"style":1212},[652],[607,2139,1150],{"className":2140},[1216],[607,2142,2119],{"className":2143},[657],[607,2145,2147,2150],{"className":2146},[1416],[607,2148,1197],{"className":2149},[1416],[607,2151,2153],{"className":2152},[668],[607,2154,2156,2176],{"className":2155},[672,1229],[607,2157,2159,2173],{"className":2158},[676],[607,2160,2162],{"className":2161,"style":1236},[680],[607,2163,2164,2167],{"style":1239},[607,2165],{"className":2166,"style":688},[687],[607,2168,2170],{"className":2169},[692,693,694,695],[607,2171,781],{"className":2172},[657,695],[607,2174,1262],{"className":2175},[1261],[607,2177,2179],{"className":2178},[676],[607,2180,2182],{"className":2181,"style":1370},[680],[607,2183],{}," pour le binaire, ",[607,2186,2188,2212],{"className":2187},[610],[607,2189,2191],{"className":2190},[614],[616,2192,2193],{"xmlns":618},[620,2194,2195,2209],{},[623,2196,2197,2199,2201,2203],{},[941,2198,1150],{"stretchy":1149},[629,2200,781],{},[875,2202,2034],{},[1152,2204,2205,2207],{},[941,2206,1197],{"stretchy":1149},[629,2208,1944],{},[636,2210,2211],{"encoding":638},"(2B)_{16}",[607,2213,2215],{"className":2214,"ariaHidden":644},[643],[607,2216,2218,2221,2224,2227,2231],{"className":2217},[648],[607,2219],{"className":2220,"style":1212},[652],[607,2222,1150],{"className":2223},[1216],[607,2225,781],{"className":2226},[657],[607,2228,2034],{"className":2229,"style":2230},[657,893],"margin-right:0.0502em;",[607,2232,2234,2237],{"className":2233},[1416],[607,2235,1197],{"className":2236},[1416],[607,2238,2240],{"className":2239},[668],[607,2241,2243,2266],{"className":2242},[672,1229],[607,2244,2246,2263],{"className":2245},[676],[607,2247,2249],{"className":2248,"style":1236},[680],[607,2250,2251,2254],{"style":1239},[607,2252],{"className":2253,"style":688},[687],[607,2255,2257],{"className":2256},[692,693,694,695],[607,2258,2260],{"className":2259},[657,695],[607,2261,1944],{"className":2262},[657,695],[607,2264,1262],{"className":2265},[1261],[607,2267,2269],{"className":2268},[676],[607,2270,2272],{"className":2271,"style":1370},[680],[607,2273],{}," pour l'hexadécimal. En Python, les\npréfixes ",[1893,2276,1902],{},[1893,2278,1922],{},[1893,2280,1965],{}," jouent le même rôle.",[593,2283,2285],{"id":2284},"du-binaire-au-décimal","Du binaire au décimal",[598,2287,2288,2289,2292],{},"Pour convertir une écriture binaire en décimal, on ",[602,2290,2291],{},"somme les puissances de\n2"," correspondant aux bits valant 1.",[598,2294,2295,2296,2096],{},"Exemple : convertir ",[607,2297,2299,2320],{"className":2298},[610],[607,2300,2302],{"className":2301},[614],[616,2303,2304],{"xmlns":618},[620,2305,2306,2318],{},[623,2307,2308,2310,2312],{},[941,2309,1150],{"stretchy":1149},[629,2311,2119],{},[1152,2313,2314,2316],{},[941,2315,1197],{"stretchy":1149},[629,2317,781],{},[636,2319,2128],{"encoding":638},[607,2321,2323],{"className":2322,"ariaHidden":644},[643],[607,2324,2326,2329,2332,2335],{"className":2325},[648],[607,2327],{"className":2328,"style":1212},[652],[607,2330,1150],{"className":2331},[1216],[607,2333,2119],{"className":2334},[657],[607,2336,2338,2341],{"className":2337},[1416],[607,2339,1197],{"className":2340},[1416],[607,2342,2344],{"className":2343},[668],[607,2345,2347,2367],{"className":2346},[672,1229],[607,2348,2350,2364],{"className":2349},[676],[607,2351,2353],{"className":2352,"style":1236},[680],[607,2354,2355,2358],{"style":1239},[607,2356],{"className":2357,"style":688},[687],[607,2359,2361],{"className":2360},[692,693,694,695],[607,2362,781],{"className":2363},[657,695],[607,2365,1262],{"className":2366},[1261],[607,2368,2370],{"className":2369},[676],[607,2371,2373],{"className":2372,"style":1370},[680],[607,2374],{},[607,2376,2378],{"className":2377},[1595],[607,2379,2381,2473],{"className":2380},[610],[607,2382,2384],{"className":2383},[614],[616,2385,2386],{"xmlns":618,"display":1604},[620,2387,2388,2470],{},[623,2389,2390,2392,2394,2400,2402,2404,2406,2413,2416,2418,2420,2426,2428,2430,2432,2438,2440,2442,2444,2450,2452,2454,2456,2458,2460,2462,2464,2466,2468],{},[941,2391,1150],{"stretchy":1149},[629,2393,2119],{},[1152,2395,2396,2398],{},[941,2397,1197],{"stretchy":1149},[629,2399,781],{},[941,2401,1614],{},[629,2403,658],{},[941,2405,1645],{},[626,2407,2408,2410],{},[629,2409,781],{},[629,2411,2412],{},"3",[941,2414,2415],{},"+",[629,2417,634],{},[941,2419,1645],{},[626,2421,2422,2424],{},[629,2423,781],{},[629,2425,781],{},[941,2427,2415],{},[629,2429,658],{},[941,2431,1645],{},[626,2433,2434,2436],{},[629,2435,781],{},[629,2437,658],{},[941,2439,2415],{},[629,2441,658],{},[941,2443,1645],{},[626,2445,2446,2448],{},[629,2447,781],{},[629,2449,634],{},[941,2451,1614],{},[629,2453,1907],{},[941,2455,2415],{},[629,2457,634],{},[941,2459,2415],{},[629,2461,781],{},[941,2463,2415],{},[629,2465,658],{},[941,2467,1614],{},[629,2469,2050],{},[636,2471,2472],{"encoding":638},"(1011)_2 = 1 \\cdot 2^3 + 0 \\cdot 2^2 + 1 \\cdot 2^1 + 1 \\cdot 2^0 = 8 + 0 + 2 + 1 = 11",[607,2474,2476,2537,2555,2601,2619,2663,2681,2725,2743,2787,2806,2824,2842,2860],{"className":2475,"ariaHidden":644},[643],[607,2477,2479,2482,2485,2488,2528,2531,2534],{"className":2478},[648],[607,2480],{"className":2481,"style":1212},[652],[607,2483,1150],{"className":2484},[1216],[607,2486,2119],{"className":2487},[657],[607,2489,2491,2494],{"className":2490},[1416],[607,2492,1197],{"className":2493},[1416],[607,2495,2497],{"className":2496},[668],[607,2498,2500,2520],{"className":2499},[672,1229],[607,2501,2503,2517],{"className":2502},[676],[607,2504,2506],{"className":2505,"style":1236},[680],[607,2507,2508,2511],{"style":1239},[607,2509],{"className":2510,"style":688},[687],[607,2512,2514],{"className":2513},[692,693,694,695],[607,2515,781],{"className":2516},[657,695],[607,2518,1262],{"className":2519},[1261],[607,2521,2523],{"className":2522},[676],[607,2524,2526],{"className":2525,"style":1370},[680],[607,2527],{},[607,2529],{"className":2530,"style":966},[965],[607,2532,1614],{"className":2533},[970],[607,2535],{"className":2536,"style":966},[965],[607,2538,2540,2543,2546,2549,2552],{"className":2539},[648],[607,2541],{"className":2542,"style":980},[652],[607,2544,658],{"className":2545},[657],[607,2547],{"className":2548,"style":1081},[965],[607,2550,1645],{"className":2551},[1085],[607,2553],{"className":2554,"style":1081},[965],[607,2556,2558,2562,2592,2595,2598],{"className":2557},[648],[607,2559],{"className":2560,"style":2561},[652],"height:0.9474em;vertical-align:-0.0833em;",[607,2563,2565,2568],{"className":2564},[657],[607,2566,781],{"className":2567},[657],[607,2569,2571],{"className":2570},[668],[607,2572,2574],{"className":2573},[672],[607,2575,2577],{"className":2576},[676],[607,2578,2581],{"className":2579,"style":2580},[680],"height:0.8641em;",[607,2582,2583,2586],{"style":1847},[607,2584],{"className":2585,"style":688},[687],[607,2587,2589],{"className":2588},[692,693,694,695],[607,2590,2412],{"className":2591},[657,695],[607,2593],{"className":2594,"style":1081},[965],[607,2596,2415],{"className":2597},[1085],[607,2599],{"className":2600,"style":1081},[965],[607,2602,2604,2607,2610,2613,2616],{"className":2603},[648],[607,2605],{"className":2606,"style":980},[652],[607,2608,634],{"className":2609},[657],[607,2611],{"className":2612,"style":1081},[965],[607,2614,1645],{"className":2615},[1085],[607,2617],{"className":2618,"style":1081},[965],[607,2620,2622,2625,2654,2657,2660],{"className":2621},[648],[607,2623],{"className":2624,"style":2561},[652],[607,2626,2628,2631],{"className":2627},[657],[607,2629,781],{"className":2630},[657],[607,2632,2634],{"className":2633},[668],[607,2635,2637],{"className":2636},[672],[607,2638,2640],{"className":2639},[676],[607,2641,2643],{"className":2642,"style":2580},[680],[607,2644,2645,2648],{"style":1847},[607,2646],{"className":2647,"style":688},[687],[607,2649,2651],{"className":2650},[692,693,694,695],[607,2652,781],{"className":2653},[657,695],[607,2655],{"className":2656,"style":1081},[965],[607,2658,2415],{"className":2659},[1085],[607,2661],{"className":2662,"style":1081},[965],[607,2664,2666,2669,2672,2675,2678],{"className":2665},[648],[607,2667],{"className":2668,"style":980},[652],[607,2670,658],{"className":2671},[657],[607,2673],{"className":2674,"style":1081},[965],[607,2676,1645],{"className":2677},[1085],[607,2679],{"className":2680,"style":1081},[965],[607,2682,2684,2687,2716,2719,2722],{"className":2683},[648],[607,2685],{"className":2686,"style":2561},[652],[607,2688,2690,2693],{"className":2689},[657],[607,2691,781],{"className":2692},[657],[607,2694,2696],{"className":2695},[668],[607,2697,2699],{"className":2698},[672],[607,2700,2702],{"className":2701},[676],[607,2703,2705],{"className":2704,"style":2580},[680],[607,2706,2707,2710],{"style":1847},[607,2708],{"className":2709,"style":688},[687],[607,2711,2713],{"className":2712},[692,693,694,695],[607,2714,658],{"className":2715},[657,695],[607,2717],{"className":2718,"style":1081},[965],[607,2720,2415],{"className":2721},[1085],[607,2723],{"className":2724,"style":1081},[965],[607,2726,2728,2731,2734,2737,2740],{"className":2727},[648],[607,2729],{"className":2730,"style":980},[652],[607,2732,658],{"className":2733},[657],[607,2735],{"className":2736,"style":1081},[965],[607,2738,1645],{"className":2739},[1085],[607,2741],{"className":2742,"style":1081},[965],[607,2744,2746,2749,2778,2781,2784],{"className":2745},[648],[607,2747],{"className":2748,"style":2580},[652],[607,2750,2752,2755],{"className":2751},[657],[607,2753,781],{"className":2754},[657],[607,2756,2758],{"className":2757},[668],[607,2759,2761],{"className":2760},[672],[607,2762,2764],{"className":2763},[676],[607,2765,2767],{"className":2766,"style":2580},[680],[607,2768,2769,2772],{"style":1847},[607,2770],{"className":2771,"style":688},[687],[607,2773,2775],{"className":2774},[692,693,694,695],[607,2776,634],{"className":2777},[657,695],[607,2779],{"className":2780,"style":966},[965],[607,2782,1614],{"className":2783},[970],[607,2785],{"className":2786,"style":966},[965],[607,2788,2790,2794,2797,2800,2803],{"className":2789},[648],[607,2791],{"className":2792,"style":2793},[652],"height:0.7278em;vertical-align:-0.0833em;",[607,2795,1907],{"className":2796},[657],[607,2798],{"className":2799,"style":1081},[965],[607,2801,2415],{"className":2802},[1085],[607,2804],{"className":2805,"style":1081},[965],[607,2807,2809,2812,2815,2818,2821],{"className":2808},[648],[607,2810],{"className":2811,"style":2793},[652],[607,2813,634],{"className":2814},[657],[607,2816],{"className":2817,"style":1081},[965],[607,2819,2415],{"className":2820},[1085],[607,2822],{"className":2823,"style":1081},[965],[607,2825,2827,2830,2833,2836,2839],{"className":2826},[648],[607,2828],{"className":2829,"style":2793},[652],[607,2831,781],{"className":2832},[657],[607,2834],{"className":2835,"style":1081},[965],[607,2837,2415],{"className":2838},[1085],[607,2840],{"className":2841,"style":1081},[965],[607,2843,2845,2848,2851,2854,2857],{"className":2844},[648],[607,2846],{"className":2847,"style":980},[652],[607,2849,658],{"className":2850},[657],[607,2852],{"className":2853,"style":966},[965],[607,2855,1614],{"className":2856},[970],[607,2858],{"className":2859,"style":966},[965],[607,2861,2863,2866],{"className":2862},[648],[607,2864],{"className":2865,"style":980},[652],[607,2867,2050],{"className":2868},[657],[598,2870,2871,2872,2875],{},"Python sait faire cette conversion automatiquement grâce à ",[1893,2873,2874],{},"int()"," avec sa\nbase passée en second argument :",[2877,2878,2883],"pre",{"className":2879,"code":2880,"language":2881,"meta":2882,"style":2882},"language-python shiki shiki-themes github-light github-light github-dark","print(int(\"1011\", 2))  # 11\nprint(int(\"FF\", 16))   # 255\nprint(int(\"17\", 8))    # 15\n","python","",[1893,2884,2885,2916,2940],{"__ignoreMap":2882},[607,2886,2889,2893,2896,2899,2901,2905,2907,2909,2912],{"class":2887,"line":2888},"line",1,[607,2890,2892],{"class":2891},"sBjJW","print",[607,2894,1150],{"class":2895},"sxrX7",[607,2897,2898],{"class":2891},"int",[607,2900,1150],{"class":2895},[607,2902,2904],{"class":2903},"sIIMD","\"1011\"",[607,2906,1895],{"class":2895},[607,2908,781],{"class":2891},[607,2910,2911],{"class":2895},"))  ",[607,2913,2915],{"class":2914},"sCsY4","# 11\n",[607,2917,2919,2921,2923,2925,2927,2930,2932,2934,2937],{"class":2887,"line":2918},2,[607,2920,2892],{"class":2891},[607,2922,1150],{"class":2895},[607,2924,2898],{"class":2891},[607,2926,1150],{"class":2895},[607,2928,2929],{"class":2903},"\"FF\"",[607,2931,1895],{"class":2895},[607,2933,1944],{"class":2891},[607,2935,2936],{"class":2895},"))   ",[607,2938,2939],{"class":2914},"# 255\n",[607,2941,2943,2945,2947,2949,2951,2954,2956,2958,2961],{"class":2887,"line":2942},3,[607,2944,2892],{"class":2891},[607,2946,1150],{"class":2895},[607,2948,2898],{"class":2891},[607,2950,1150],{"class":2895},[607,2952,2953],{"class":2903},"\"17\"",[607,2955,1895],{"class":2895},[607,2957,1907],{"class":2891},[607,2959,2960],{"class":2895},"))    ",[607,2962,2963],{"class":2914},"# 15\n",[2965,2966,2968,3056],"self-eval-qcm",{"correct":658,"slug":2967},"bases-entiers-positifs-c1",[2969,2970,2971],"template",{"v-slot:question":2882},[598,2972,2973,2974,3055],{},"Que vaut ",[607,2975,2977,3000],{"className":2976},[610],[607,2978,2980],{"className":2979},[614],[616,2981,2982],{"xmlns":618},[620,2983,2984,2997],{},[623,2985,2986,2988,2991],{},[941,2987,1150],{"stretchy":1149},[629,2989,2990],{},"1101",[1152,2992,2993,2995],{},[941,2994,1197],{"stretchy":1149},[629,2996,781],{},[636,2998,2999],{"encoding":638},"(1101)_2",[607,3001,3003],{"className":3002,"ariaHidden":644},[643],[607,3004,3006,3009,3012,3015],{"className":3005},[648],[607,3007],{"className":3008,"style":1212},[652],[607,3010,1150],{"className":3011},[1216],[607,3013,2990],{"className":3014},[657],[607,3016,3018,3021],{"className":3017},[1416],[607,3019,1197],{"className":3020},[1416],[607,3022,3024],{"className":3023},[668],[607,3025,3027,3047],{"className":3026},[672,1229],[607,3028,3030,3044],{"className":3029},[676],[607,3031,3033],{"className":3032,"style":1236},[680],[607,3034,3035,3038],{"style":1239},[607,3036],{"className":3037,"style":688},[687],[607,3039,3041],{"className":3040},[692,693,694,695],[607,3042,781],{"className":3043},[657,695],[607,3045,1262],{"className":3046},[1261],[607,3048,3050],{"className":3049},[676],[607,3051,3053],{"className":3052,"style":1370},[680],[607,3054],{}," en décimal ?",[2969,3057,3058],{"v-slot:choices":2882},[3059,3060,3061,3064,3067,3070],"ul",{},[3062,3063,2050],"li",{},[3062,3065,3066],{},"13",[3062,3068,3069],{},"14",[3062,3071,2016],{},[593,3073,3075],{"id":3074},"du-décimal-au-binaire-les-divisions-successives","Du décimal au binaire — les divisions successives",[598,3077,3078,3079,3082,3083,3086],{},"Pour passer du décimal au binaire, on divise le nombre par 2 et on note le\n",[602,3080,3081],{},"reste",". On répète l'opération sur le quotient jusqu'à obtenir 0. La lecture\ndes restes ",[602,3084,3085],{},"de bas en haut"," donne l'écriture binaire.",[598,3088,2295,3089,3117],{},[607,3090,3092,3105],{"className":3091},[610],[607,3093,3095],{"className":3094},[614],[616,3096,3097],{"xmlns":618},[620,3098,3099,3103],{},[623,3100,3101],{},[629,3102,3066],{},[636,3104,3066],{"encoding":638},[607,3106,3108],{"className":3107,"ariaHidden":644},[643],[607,3109,3111,3114],{"className":3110},[648],[607,3112],{"className":3113,"style":980},[652],[607,3115,3066],{"className":3116},[657]," en binaire.",[1858,3119,3120,3133],{},[1861,3121,3122],{},[1864,3123,3124,3127,3130],{},[1867,3125,3126],{},"Division",[1867,3128,3129],{},"Quotient",[1867,3131,3132],{},"Reste",[1880,3134,3135,3255,3371,3486],{},[1864,3136,3137,3191,3222],{},[1885,3138,3139],{},[607,3140,3142,3161],{"className":3141},[610],[607,3143,3145],{"className":3144},[614],[616,3146,3147],{"xmlns":618},[620,3148,3149,3158],{},[623,3150,3151,3153,3156],{},[629,3152,3066],{},[941,3154,3155],{},"÷",[629,3157,781],{},[636,3159,3160],{"encoding":638},"13 \\div 2",[607,3162,3164,3182],{"className":3163,"ariaHidden":644},[643],[607,3165,3167,3170,3173,3176,3179],{"className":3166},[648],[607,3168],{"className":3169,"style":2793},[652],[607,3171,3066],{"className":3172},[657],[607,3174],{"className":3175,"style":1081},[965],[607,3177,3155],{"className":3178},[1085],[607,3180],{"className":3181,"style":1081},[965],[607,3183,3185,3188],{"className":3184},[648],[607,3186],{"className":3187,"style":980},[652],[607,3189,781],{"className":3190},[657],[1885,3192,3193],{},[607,3194,3196,3210],{"className":3195},[610],[607,3197,3199],{"className":3198},[614],[616,3200,3201],{"xmlns":618},[620,3202,3203,3208],{},[623,3204,3205],{},[629,3206,3207],{},"6",[636,3209,3207],{"encoding":638},[607,3211,3213],{"className":3212,"ariaHidden":644},[643],[607,3214,3216,3219],{"className":3215},[648],[607,3217],{"className":3218,"style":980},[652],[607,3220,3207],{"className":3221},[657],[1885,3223,3224],{},[607,3225,3227,3242],{"className":3226},[610],[607,3228,3230],{"className":3229},[614],[616,3231,3232],{"xmlns":618},[620,3233,3234,3239],{},[623,3235,3236],{},[629,3237,658],{"mathvariant":3238},"bold",[636,3240,3241],{"encoding":638},"\\mathbf{1}",[607,3243,3245],{"className":3244,"ariaHidden":644},[643],[607,3246,3248,3251],{"className":3247},[648],[607,3249],{"className":3250,"style":980},[652],[607,3252,658],{"className":3253},[657,3254],"mathbf",[1864,3256,3257,3310,3340],{},[1885,3258,3259],{},[607,3260,3262,3280],{"className":3261},[610],[607,3263,3265],{"className":3264},[614],[616,3266,3267],{"xmlns":618},[620,3268,3269,3277],{},[623,3270,3271,3273,3275],{},[629,3272,3207],{},[941,3274,3155],{},[629,3276,781],{},[636,3278,3279],{"encoding":638},"6 \\div 2",[607,3281,3283,3301],{"className":3282,"ariaHidden":644},[643],[607,3284,3286,3289,3292,3295,3298],{"className":3285},[648],[607,3287],{"className":3288,"style":2793},[652],[607,3290,3207],{"className":3291},[657],[607,3293],{"className":3294,"style":1081},[965],[607,3296,3155],{"className":3297},[1085],[607,3299],{"className":3300,"style":1081},[965],[607,3302,3304,3307],{"className":3303},[648],[607,3305],{"className":3306,"style":980},[652],[607,3308,781],{"className":3309},[657],[1885,3311,3312],{},[607,3313,3315,3328],{"className":3314},[610],[607,3316,3318],{"className":3317},[614],[616,3319,3320],{"xmlns":618},[620,3321,3322,3326],{},[623,3323,3324],{},[629,3325,2412],{},[636,3327,2412],{"encoding":638},[607,3329,3331],{"className":3330,"ariaHidden":644},[643],[607,3332,3334,3337],{"className":3333},[648],[607,3335],{"className":3336,"style":980},[652],[607,3338,2412],{"className":3339},[657],[1885,3341,3342],{},[607,3343,3345,3359],{"className":3344},[610],[607,3346,3348],{"className":3347},[614],[616,3349,3350],{"xmlns":618},[620,3351,3352,3356],{},[623,3353,3354],{},[629,3355,634],{"mathvariant":3238},[636,3357,3358],{"encoding":638},"\\mathbf{0}",[607,3360,3362],{"className":3361,"ariaHidden":644},[643],[607,3363,3365,3368],{"className":3364},[648],[607,3366],{"className":3367,"style":980},[652],[607,3369,634],{"className":3370},[657,3254],[1864,3372,3373,3426,3456],{},[1885,3374,3375],{},[607,3376,3378,3396],{"className":3377},[610],[607,3379,3381],{"className":3380},[614],[616,3382,3383],{"xmlns":618},[620,3384,3385,3393],{},[623,3386,3387,3389,3391],{},[629,3388,2412],{},[941,3390,3155],{},[629,3392,781],{},[636,3394,3395],{"encoding":638},"3 \\div 2",[607,3397,3399,3417],{"className":3398,"ariaHidden":644},[643],[607,3400,3402,3405,3408,3411,3414],{"className":3401},[648],[607,3403],{"className":3404,"style":2793},[652],[607,3406,2412],{"className":3407},[657],[607,3409],{"className":3410,"style":1081},[965],[607,3412,3155],{"className":3413},[1085],[607,3415],{"className":3416,"style":1081},[965],[607,3418,3420,3423],{"className":3419},[648],[607,3421],{"className":3422,"style":980},[652],[607,3424,781],{"className":3425},[657],[1885,3427,3428],{},[607,3429,3431,3444],{"className":3430},[610],[607,3432,3434],{"className":3433},[614],[616,3435,3436],{"xmlns":618},[620,3437,3438,3442],{},[623,3439,3440],{},[629,3441,658],{},[636,3443,658],{"encoding":638},[607,3445,3447],{"className":3446,"ariaHidden":644},[643],[607,3448,3450,3453],{"className":3449},[648],[607,3451],{"className":3452,"style":980},[652],[607,3454,658],{"className":3455},[657],[1885,3457,3458],{},[607,3459,3461,3474],{"className":3460},[610],[607,3462,3464],{"className":3463},[614],[616,3465,3466],{"xmlns":618},[620,3467,3468,3472],{},[623,3469,3470],{},[629,3471,658],{"mathvariant":3238},[636,3473,3241],{"encoding":638},[607,3475,3477],{"className":3476,"ariaHidden":644},[643],[607,3478,3480,3483],{"className":3479},[648],[607,3481],{"className":3482,"style":980},[652],[607,3484,658],{"className":3485},[657,3254],[1864,3487,3488,3541,3571],{},[1885,3489,3490],{},[607,3491,3493,3511],{"className":3492},[610],[607,3494,3496],{"className":3495},[614],[616,3497,3498],{"xmlns":618},[620,3499,3500,3508],{},[623,3501,3502,3504,3506],{},[629,3503,658],{},[941,3505,3155],{},[629,3507,781],{},[636,3509,3510],{"encoding":638},"1 \\div 2",[607,3512,3514,3532],{"className":3513,"ariaHidden":644},[643],[607,3515,3517,3520,3523,3526,3529],{"className":3516},[648],[607,3518],{"className":3519,"style":2793},[652],[607,3521,658],{"className":3522},[657],[607,3524],{"className":3525,"style":1081},[965],[607,3527,3155],{"className":3528},[1085],[607,3530],{"className":3531,"style":1081},[965],[607,3533,3535,3538],{"className":3534},[648],[607,3536],{"className":3537,"style":980},[652],[607,3539,781],{"className":3540},[657],[1885,3542,3543],{},[607,3544,3546,3559],{"className":3545},[610],[607,3547,3549],{"className":3548},[614],[616,3550,3551],{"xmlns":618},[620,3552,3553,3557],{},[623,3554,3555],{},[629,3556,634],{},[636,3558,634],{"encoding":638},[607,3560,3562],{"className":3561,"ariaHidden":644},[643],[607,3563,3565,3568],{"className":3564},[648],[607,3566],{"className":3567,"style":980},[652],[607,3569,634],{"className":3570},[657],[1885,3572,3573],{},[607,3574,3576,3589],{"className":3575},[610],[607,3577,3579],{"className":3578},[614],[616,3580,3581],{"xmlns":618},[620,3582,3583,3587],{},[623,3584,3585],{},[629,3586,658],{"mathvariant":3238},[636,3588,3241],{"encoding":638},[607,3590,3592],{"className":3591,"ariaHidden":644},[643],[607,3593,3595,3598],{"className":3594},[648],[607,3596],{"className":3597,"style":980},[652],[607,3599,658],{"className":3600},[657,3254],[598,3602,3603,3604,2096],{},"En lisant les restes de bas en haut : ",[607,3605,3607,3633],{"className":3606},[610],[607,3608,3610],{"className":3609},[614],[616,3611,3612],{"xmlns":618},[620,3613,3614,3630],{},[623,3615,3616,3618,3620,3622,3624],{},[629,3617,3066],{},[941,3619,1614],{},[941,3621,1150],{"stretchy":1149},[629,3623,2990],{},[1152,3625,3626,3628],{},[941,3627,1197],{"stretchy":1149},[629,3629,781],{},[636,3631,3632],{"encoding":638},"13 = (1101)_2",[607,3634,3636,3654],{"className":3635,"ariaHidden":644},[643],[607,3637,3639,3642,3645,3648,3651],{"className":3638},[648],[607,3640],{"className":3641,"style":980},[652],[607,3643,3066],{"className":3644},[657],[607,3646],{"className":3647,"style":966},[965],[607,3649,1614],{"className":3650},[970],[607,3652],{"className":3653,"style":966},[965],[607,3655,3657,3660,3663,3666],{"className":3656},[648],[607,3658],{"className":3659,"style":1212},[652],[607,3661,1150],{"className":3662},[1216],[607,3664,2990],{"className":3665},[657],[607,3667,3669,3672],{"className":3668},[1416],[607,3670,1197],{"className":3671},[1416],[607,3673,3675],{"className":3674},[668],[607,3676,3678,3698],{"className":3677},[672,1229],[607,3679,3681,3695],{"className":3680},[676],[607,3682,3684],{"className":3683,"style":1236},[680],[607,3685,3686,3689],{"style":1239},[607,3687],{"className":3688,"style":688},[687],[607,3690,3692],{"className":3691},[692,693,694,695],[607,3693,781],{"className":3694},[657,695],[607,3696,1262],{"className":3697},[1261],[607,3699,3701],{"className":3700},[676],[607,3702,3704],{"className":3703,"style":1370},[680],[607,3705],{},[3707,3708,3709],"python-snippet",{},[2877,3710,3712],{"className":2879,"code":3711,"language":2881,"meta":2882,"style":2882},"n = 13\nprint(f\"{n} en binaire : {bin(n)}\")\nprint(f\"{n} en hexadécimal : {hex(n)}\")\nprint(f\"{n} en octal : {oct(n)}\")\n",[1893,3713,3714,3725,3761,3791],{"__ignoreMap":2882},[607,3715,3716,3719,3722],{"class":2887,"line":2888},[607,3717,3718],{"class":2895},"n ",[607,3720,1614],{"class":3721},"s8jYJ",[607,3723,3724],{"class":2891}," 13\n",[607,3726,3727,3729,3731,3734,3737,3740,3742,3745,3748,3751,3754,3756,3758],{"class":2887,"line":2918},[607,3728,2892],{"class":2891},[607,3730,1150],{"class":2895},[607,3732,3733],{"class":3721},"f",[607,3735,3736],{"class":2903},"\"",[607,3738,3739],{"class":2891},"{",[607,3741,1161],{"class":2895},[607,3743,3744],{"class":2891},"}",[607,3746,3747],{"class":2903}," en binaire : ",[607,3749,3750],{"class":2891},"{bin",[607,3752,3753],{"class":2895},"(n)",[607,3755,3744],{"class":2891},[607,3757,3736],{"class":2903},[607,3759,3760],{"class":2895},")\n",[607,3762,3763,3765,3767,3769,3771,3773,3775,3777,3780,3783,3785,3787,3789],{"class":2887,"line":2942},[607,3764,2892],{"class":2891},[607,3766,1150],{"class":2895},[607,3768,3733],{"class":3721},[607,3770,3736],{"class":2903},[607,3772,3739],{"class":2891},[607,3774,1161],{"class":2895},[607,3776,3744],{"class":2891},[607,3778,3779],{"class":2903}," en hexadécimal : ",[607,3781,3782],{"class":2891},"{hex",[607,3784,3753],{"class":2895},[607,3786,3744],{"class":2891},[607,3788,3736],{"class":2903},[607,3790,3760],{"class":2895},[607,3792,3794,3796,3798,3800,3802,3804,3806,3808,3811,3814,3816,3818,3820],{"class":2887,"line":3793},4,[607,3795,2892],{"class":2891},[607,3797,1150],{"class":2895},[607,3799,3733],{"class":3721},[607,3801,3736],{"class":2903},[607,3803,3739],{"class":2891},[607,3805,1161],{"class":2895},[607,3807,3744],{"class":2891},[607,3809,3810],{"class":2903}," en octal : ",[607,3812,3813],{"class":2891},"{oct",[607,3815,3753],{"class":2895},[607,3817,3744],{"class":2891},[607,3819,3736],{"class":2903},[607,3821,3760],{"class":2895},[598,3823,3824],{},"Sortie attendue :",[2877,3826,3831],{"className":3827,"code":3829,"language":3830},[3828],"language-text","13 en binaire : 0b1101\n13 en hexadécimal : 0xd\n13 en octal : 0o15\n","text",[1893,3832,3829],{"__ignoreMap":2882},[593,3834,3836],{"id":3835},"le-pont-avec-lhexadécimal","Le pont avec l'hexadécimal",[598,3838,3839,3840,3843],{},"L'hexadécimal a un atout précieux : ",[602,3841,3842],{},"chaque chiffre hexadécimal correspond\nexactement à 4 bits",". La conversion binaire ↔ hexadécimal se fait donc par\nblocs, sans aucun calcul.",[1858,3845,3846,3860],{},[1861,3847,3848],{},[1864,3849,3850,3853,3856,3858],{},[1867,3851,3852],{},"Hex",[1867,3854,3855],{},"Binaire",[1867,3857,3852],{},[1867,3859,3855],{},[1880,3861,3862,3882,3902,3922,3941,3963,3984,4005],{},[1864,3863,3864,3868,3873,3877],{},[1885,3865,3866],{},[1893,3867,634],{},[1885,3869,3870],{},[1893,3871,3872],{},"0000",[1885,3874,3875],{},[1893,3876,1907],{},[1885,3878,3879],{},[1893,3880,3881],{},"1000",[1864,3883,3884,3888,3893,3897],{},[1885,3885,3886],{},[1893,3887,658],{},[1885,3889,3890],{},[1893,3891,3892],{},"0001",[1885,3894,3895],{},[1893,3896,1936],{},[1885,3898,3899],{},[1893,3900,3901],{},"1001",[1864,3903,3904,3908,3913,3917],{},[1885,3905,3906],{},[1893,3907,781],{},[1885,3909,3910],{},[1893,3911,3912],{},"0010",[1885,3914,3915],{},[1893,3916,1957],{},[1885,3918,3919],{},[1893,3920,3921],{},"1010",[1864,3923,3924,3928,3933,3937],{},[1885,3925,3926],{},[1893,3927,2412],{},[1885,3929,3930],{},[1893,3931,3932],{},"0011",[1885,3934,3935],{},[1893,3936,2034],{},[1885,3938,3939],{},[1893,3940,2119],{},[1864,3942,3943,3948,3953,3958],{},[1885,3944,3945],{},[1893,3946,3947],{},"4",[1885,3949,3950],{},[1893,3951,3952],{},"0100",[1885,3954,3955],{},[1893,3956,3957],{},"C",[1885,3959,3960],{},[1893,3961,3962],{},"1100",[1864,3964,3965,3970,3975,3980],{},[1885,3966,3967],{},[1893,3968,3969],{},"5",[1885,3971,3972],{},[1893,3973,3974],{},"0101",[1885,3976,3977],{},[1893,3978,3979],{},"D",[1885,3981,3982],{},[1893,3983,2990],{},[1864,3985,3986,3990,3995,4000],{},[1885,3987,3988],{},[1893,3989,3207],{},[1885,3991,3992],{},[1893,3993,3994],{},"0110",[1885,3996,3997],{},[1893,3998,3999],{},"E",[1885,4001,4002],{},[1893,4003,4004],{},"1110",[1864,4006,4007,4011,4016,4020],{},[1885,4008,4009],{},[1893,4010,1917],{},[1885,4012,4013],{},[1893,4014,4015],{},"0111",[1885,4017,4018],{},[1893,4019,1960],{},[1885,4021,4022],{},[1893,4023,4024],{},"1111",[598,4026,4027,4028,2096],{},"Exemple : ",[607,4029,4031,4078],{"className":4030},[610],[607,4032,4034],{"className":4033},[614],[616,4035,4036],{"xmlns":618},[620,4037,4038,4075],{},[623,4039,4040,4042,4044,4046,4052,4054,4056,4058,4062,4064,4070,4072],{},[941,4041,1150],{"stretchy":1149},[629,4043,781],{},[875,4045,1960],{},[1152,4047,4048,4050],{},[941,4049,1197],{"stretchy":1149},[629,4051,1944],{},[941,4053,1614],{},[941,4055,1150],{"stretchy":1149},[629,4057,3912],{},[4059,4060,4061],"mtext",{}," ",[629,4063,4024],{},[1152,4065,4066,4068],{},[941,4067,1197],{"stretchy":1149},[629,4069,781],{},[941,4071,1614],{},[629,4073,4074],{},"47",[636,4076,4077],{"encoding":638},"(2F)_{16} = (0010\\ 1111)_2 = 47",[607,4079,4081,4149,4216],{"className":4080,"ariaHidden":644},[643],[607,4082,4084,4087,4090,4093,4097,4140,4143,4146],{"className":4083},[648],[607,4085],{"className":4086,"style":1212},[652],[607,4088,1150],{"className":4089},[1216],[607,4091,781],{"className":4092},[657],[607,4094,1960],{"className":4095,"style":4096},[657,893],"margin-right:0.1389em;",[607,4098,4100,4103],{"className":4099},[1416],[607,4101,1197],{"className":4102},[1416],[607,4104,4106],{"className":4105},[668],[607,4107,4109,4132],{"className":4108},[672,1229],[607,4110,4112,4129],{"className":4111},[676],[607,4113,4115],{"className":4114,"style":1236},[680],[607,4116,4117,4120],{"style":1239},[607,4118],{"className":4119,"style":688},[687],[607,4121,4123],{"className":4122},[692,693,694,695],[607,4124,4126],{"className":4125},[657,695],[607,4127,1944],{"className":4128},[657,695],[607,4130,1262],{"className":4131},[1261],[607,4133,4135],{"className":4134},[676],[607,4136,4138],{"className":4137,"style":1370},[680],[607,4139],{},[607,4141],{"className":4142,"style":966},[965],[607,4144,1614],{"className":4145},[970],[607,4147],{"className":4148,"style":966},[965],[607,4150,4152,4155,4158,4161,4164,4167,4207,4210,4213],{"className":4151},[648],[607,4153],{"className":4154,"style":1212},[652],[607,4156,1150],{"className":4157},[1216],[607,4159,3912],{"className":4160},[657],[607,4162,4061],{"className":4163},[965],[607,4165,4024],{"className":4166},[657],[607,4168,4170,4173],{"className":4169},[1416],[607,4171,1197],{"className":4172},[1416],[607,4174,4176],{"className":4175},[668],[607,4177,4179,4199],{"className":4178},[672,1229],[607,4180,4182,4196],{"className":4181},[676],[607,4183,4185],{"className":4184,"style":1236},[680],[607,4186,4187,4190],{"style":1239},[607,4188],{"className":4189,"style":688},[687],[607,4191,4193],{"className":4192},[692,693,694,695],[607,4194,781],{"className":4195},[657,695],[607,4197,1262],{"className":4198},[1261],[607,4200,4202],{"className":4201},[676],[607,4203,4205],{"className":4204,"style":1370},[680],[607,4206],{},[607,4208],{"className":4209,"style":966},[965],[607,4211,1614],{"className":4212},[970],[607,4214],{"className":4215,"style":966},[965],[607,4217,4219,4222],{"className":4218},[648],[607,4220],{"className":4221,"style":980},[652],[607,4223,4074],{"className":4224},[657],[598,4226,4227,4228,4231],{},"C'est pour cela qu'on rencontre l'hexadécimal partout en informatique :\nadresses mémoire, couleurs CSS (",[1893,4229,4230],{},"#FF8800","), valeurs d'un octet… Lire un octet\nen hexadécimal, c'est lire 2 chiffres au lieu de 8 bits.",[2965,4233,4235,4329],{"correct":781,"slug":4234},"bases-entiers-positifs-c2",[2969,4236,4237],{"v-slot:question":2882},[598,4238,4239,4240,4328],{},"Combien de bits sont nécessaires pour écrire ",[607,4241,4243,4267],{"className":4242},[610],[607,4244,4246],{"className":4245},[614],[616,4247,4248],{"xmlns":618},[620,4249,4250,4264],{},[623,4251,4252,4254,4256,4258],{},[941,4253,1150],{"stretchy":1149},[875,4255,1957],{},[629,4257,2412],{},[1152,4259,4260,4262],{},[941,4261,1197],{"stretchy":1149},[629,4263,1944],{},[636,4265,4266],{"encoding":638},"(A3)_{16}",[607,4268,4270],{"className":4269,"ariaHidden":644},[643],[607,4271,4273,4276,4279,4282,4285],{"className":4272},[648],[607,4274],{"className":4275,"style":1212},[652],[607,4277,1150],{"className":4278},[1216],[607,4280,1957],{"className":4281},[657,893],[607,4283,2412],{"className":4284},[657],[607,4286,4288,4291],{"className":4287},[1416],[607,4289,1197],{"className":4290},[1416],[607,4292,4294],{"className":4293},[668],[607,4295,4297,4320],{"className":4296},[672,1229],[607,4298,4300,4317],{"className":4299},[676],[607,4301,4303],{"className":4302,"style":1236},[680],[607,4304,4305,4308],{"style":1239},[607,4306],{"className":4307,"style":688},[687],[607,4309,4311],{"className":4310},[692,693,694,695],[607,4312,4314],{"className":4313},[657,695],[607,4315,1944],{"className":4316},[657,695],[607,4318,1262],{"className":4319},[1261],[607,4321,4323],{"className":4322},[676],[607,4324,4326],{"className":4325,"style":1370},[680],[607,4327],{}," ?",[2969,4330,4331],{"v-slot:choices":2882},[3059,4332,4333,4335,4337,4339],{},[3062,4334,3947],{},[3062,4336,3207],{},[3062,4338,1907],{},[3062,4340,1944],{},[593,4342,4344],{"id":4343},"combien-de-bits-pour-un-nombre","Combien de bits pour un nombre ?",[598,4346,4347,4348,4377,4378,4438,4439,1042,4467,2096],{},"Avec ",[607,4349,4351,4364],{"className":4350},[610],[607,4352,4354],{"className":4353},[614],[616,4355,4356],{"xmlns":618},[620,4357,4358,4362],{},[623,4359,4360],{},[875,4361,1161],{},[636,4363,1161],{"encoding":638},[607,4365,4367],{"className":4366,"ariaHidden":644},[643],[607,4368,4370,4374],{"className":4369},[648],[607,4371],{"className":4372,"style":4373},[652],"height:0.4306em;",[607,4375,1161],{"className":4376},[657,893]," bits, on peut représenter ",[607,4379,4381,4399],{"className":4380},[610],[607,4382,4384],{"className":4383},[614],[616,4385,4386],{"xmlns":618},[620,4387,4388,4396],{},[623,4389,4390],{},[626,4391,4392,4394],{},[629,4393,781],{},[875,4395,1161],{},[636,4397,4398],{"encoding":638},"2^n",[607,4400,4402],{"className":4401,"ariaHidden":644},[643],[607,4403,4405,4409],{"className":4404},[648],[607,4406],{"className":4407,"style":4408},[652],"height:0.6644em;",[607,4410,4412,4415],{"className":4411},[657],[607,4413,781],{"className":4414},[657],[607,4416,4418],{"className":4417},[668],[607,4419,4421],{"className":4420},[672],[607,4422,4424],{"className":4423},[676],[607,4425,4427],{"className":4426,"style":4408},[680],[607,4428,4429,4432],{"style":683},[607,4430],{"className":4431,"style":688},[687],[607,4433,4435],{"className":4434},[692,693,694,695],[607,4436,1161],{"className":4437},[657,893,695]," valeurs différentes, soit les entiers\nde ",[607,4440,4442,4455],{"className":4441},[610],[607,4443,4445],{"className":4444},[614],[616,4446,4447],{"xmlns":618},[620,4448,4449,4453],{},[623,4450,4451],{},[629,4452,634],{},[636,4454,634],{"encoding":638},[607,4456,4458],{"className":4457,"ariaHidden":644},[643],[607,4459,4461,4464],{"className":4460},[648],[607,4462],{"className":4463,"style":980},[652],[607,4465,634],{"className":4466},[657],[607,4468,4470,4492],{"className":4469},[610],[607,4471,4473],{"className":4472},[614],[616,4474,4475],{"xmlns":618},[620,4476,4477,4489],{},[623,4478,4479,4485,4487],{},[626,4480,4481,4483],{},[629,4482,781],{},[875,4484,1161],{},[941,4486,1059],{},[629,4488,658],{},[636,4490,4491],{"encoding":638},"2^n - 1",[607,4493,4495,4540],{"className":4494,"ariaHidden":644},[643],[607,4496,4498,4502,4531,4534,4537],{"className":4497},[648],[607,4499],{"className":4500,"style":4501},[652],"height:0.7477em;vertical-align:-0.0833em;",[607,4503,4505,4508],{"className":4504},[657],[607,4506,781],{"className":4507},[657],[607,4509,4511],{"className":4510},[668],[607,4512,4514],{"className":4513},[672],[607,4515,4517],{"className":4516},[676],[607,4518,4520],{"className":4519,"style":4408},[680],[607,4521,4522,4525],{"style":683},[607,4523],{"className":4524,"style":688},[687],[607,4526,4528],{"className":4527},[692,693,694,695],[607,4529,1161],{"className":4530},[657,893,695],[607,4532],{"className":4533,"style":1081},[965],[607,4535,1059],{"className":4536},[1085],[607,4538],{"className":4539,"style":1081},[965],[607,4541,4543,4546],{"className":4542},[648],[607,4544],{"className":4545,"style":980},[652],[607,4547,658],{"className":4548},[657],[1858,4550,4551,4564],{},[1861,4552,4553],{},[1864,4554,4555,4558,4561],{},[1867,4556,4557],{},"Bits",[1867,4559,4560],{},"Valeurs représentables",[1867,4562,4563],{},"Maximum",[1880,4565,4566,4683,4803,4948],{},[1864,4567,4568,4570,4653],{},[1885,4569,3947],{},[1885,4571,4572],{},[607,4573,4575,4597],{"className":4574},[610],[607,4576,4578],{"className":4577},[614],[616,4579,4580],{"xmlns":618},[620,4581,4582,4594],{},[623,4583,4584,4590,4592],{},[626,4585,4586,4588],{},[629,4587,781],{},[629,4589,3947],{},[941,4591,1614],{},[629,4593,1944],{},[636,4595,4596],{"encoding":638},"2^4 = 16",[607,4598,4600,4644],{"className":4599,"ariaHidden":644},[643],[607,4601,4603,4606,4635,4638,4641],{"className":4602},[648],[607,4604],{"className":4605,"style":653},[652],[607,4607,4609,4612],{"className":4608},[657],[607,4610,781],{"className":4611},[657],[607,4613,4615],{"className":4614},[668],[607,4616,4618],{"className":4617},[672],[607,4619,4621],{"className":4620},[676],[607,4622,4624],{"className":4623,"style":653},[680],[607,4625,4626,4629],{"style":683},[607,4627],{"className":4628,"style":688},[687],[607,4630,4632],{"className":4631},[692,693,694,695],[607,4633,3947],{"className":4634},[657,695],[607,4636],{"className":4637,"style":966},[965],[607,4639,1614],{"className":4640},[970],[607,4642],{"className":4643,"style":966},[965],[607,4645,4647,4650],{"className":4646},[648],[607,4648],{"className":4649,"style":980},[652],[607,4651,1944],{"className":4652},[657],[1885,4654,4655],{},[607,4656,4658,4671],{"className":4657},[610],[607,4659,4661],{"className":4660},[614],[616,4662,4663],{"xmlns":618},[620,4664,4665,4669],{},[623,4666,4667],{},[629,4668,2016],{},[636,4670,2016],{"encoding":638},[607,4672,4674],{"className":4673,"ariaHidden":644},[643],[607,4675,4677,4680],{"className":4676},[648],[607,4678],{"className":4679,"style":980},[652],[607,4681,2016],{"className":4682},[657],[1864,4684,4685,4688,4772],{},[1885,4686,4687],{},"8 (octet)",[1885,4689,4690],{},[607,4691,4693,4716],{"className":4692},[610],[607,4694,4696],{"className":4695},[614],[616,4697,4698],{"xmlns":618},[620,4699,4700,4713],{},[623,4701,4702,4708,4710],{},[626,4703,4704,4706],{},[629,4705,781],{},[629,4707,1907],{},[941,4709,1614],{},[629,4711,4712],{},"256",[636,4714,4715],{"encoding":638},"2^8 = 256",[607,4717,4719,4763],{"className":4718,"ariaHidden":644},[643],[607,4720,4722,4725,4754,4757,4760],{"className":4721},[648],[607,4723],{"className":4724,"style":653},[652],[607,4726,4728,4731],{"className":4727},[657],[607,4729,781],{"className":4730},[657],[607,4732,4734],{"className":4733},[668],[607,4735,4737],{"className":4736},[672],[607,4738,4740],{"className":4739},[676],[607,4741,4743],{"className":4742,"style":653},[680],[607,4744,4745,4748],{"style":683},[607,4746],{"className":4747,"style":688},[687],[607,4749,4751],{"className":4750},[692,693,694,695],[607,4752,1907],{"className":4753},[657,695],[607,4755],{"className":4756,"style":966},[965],[607,4758,1614],{"className":4759},[970],[607,4761],{"className":4762,"style":966},[965],[607,4764,4766,4769],{"className":4765},[648],[607,4767],{"className":4768,"style":980},[652],[607,4770,4712],{"className":4771},[657],[1885,4773,4774],{},[607,4775,4777,4791],{"className":4776},[610],[607,4778,4780],{"className":4779},[614],[616,4781,4782],{"xmlns":618},[620,4783,4784,4789],{},[623,4785,4786],{},[629,4787,4788],{},"255",[636,4790,4788],{"encoding":638},[607,4792,4794],{"className":4793,"ariaHidden":644},[643],[607,4795,4797,4800],{"className":4796},[648],[607,4798],{"className":4799,"style":980},[652],[607,4801,4788],{"className":4802},[657],[1864,4804,4805,4807,4906],{},[1885,4806,1944],{},[1885,4808,4809],{},[607,4810,4812,4841],{"className":4811},[610],[607,4813,4815],{"className":4814},[614],[616,4816,4817],{"xmlns":618},[620,4818,4819,4838],{},[623,4820,4821,4827,4829,4832,4835],{},[626,4822,4823,4825],{},[629,4824,781],{},[629,4826,1944],{},[941,4828,1614],{},[629,4830,4831],{},"65",[4059,4833,4834],{}," ",[629,4836,4837],{},"536",[636,4839,4840],{"encoding":638},"2^{16} = 65\\,536",[607,4842,4844,4891],{"className":4843,"ariaHidden":644},[643],[607,4845,4847,4850,4882,4885,4888],{"className":4846},[648],[607,4848],{"className":4849,"style":653},[652],[607,4851,4853,4856],{"className":4852},[657],[607,4854,781],{"className":4855},[657],[607,4857,4859],{"className":4858},[668],[607,4860,4862],{"className":4861},[672],[607,4863,4865],{"className":4864},[676],[607,4866,4868],{"className":4867,"style":653},[680],[607,4869,4870,4873],{"style":683},[607,4871],{"className":4872,"style":688},[687],[607,4874,4876],{"className":4875},[692,693,694,695],[607,4877,4879],{"className":4878},[657,695],[607,4880,1944],{"className":4881},[657,695],[607,4883],{"className":4884,"style":966},[965],[607,4886,1614],{"className":4887},[970],[607,4889],{"className":4890,"style":966},[965],[607,4892,4894,4897,4900,4903],{"className":4893},[648],[607,4895],{"className":4896,"style":980},[652],[607,4898,4831],{"className":4899},[657],[607,4901],{"className":4902,"style":1324},[965],[607,4904,4837],{"className":4905},[657],[1885,4907,4908],{},[607,4909,4911,4930],{"className":4910},[610],[607,4912,4914],{"className":4913},[614],[616,4915,4916],{"xmlns":618},[620,4917,4918,4927],{},[623,4919,4920,4922,4924],{},[629,4921,4831],{},[4059,4923,4834],{},[629,4925,4926],{},"535",[636,4928,4929],{"encoding":638},"65\\,535",[607,4931,4933],{"className":4932,"ariaHidden":644},[643],[607,4934,4936,4939,4942,4945],{"className":4935},[648],[607,4937],{"className":4938,"style":980},[652],[607,4940,4831],{"className":4941},[657],[607,4943],{"className":4944,"style":1324},[965],[607,4946,4926],{"className":4947},[657],[1864,4949,4950,4953,5108],{},[1885,4951,4952],{},"32",[1885,4954,4955],{},[607,4956,4958,4990],{"className":4957},[610],[607,4959,4961],{"className":4960},[614],[616,4962,4963],{"xmlns":618},[620,4964,4965,4987],{},[623,4966,4967,4973,4976,4979,4981],{},[626,4968,4969,4971],{},[629,4970,781],{},[629,4972,4952],{},[941,4974,4975],{},"≈",[629,4977,4978],{},"4,3",[941,4980,1645],{},[626,4982,4983,4985],{},[629,4984,631],{},[629,4986,1936],{},[636,4988,4989],{"encoding":638},"2^{32} \\approx 4{,}3 \\cdot 10^9",[607,4991,4993,5040,5070],{"className":4992,"ariaHidden":644},[643],[607,4994,4996,4999,5031,5034,5037],{"className":4995},[648],[607,4997],{"className":4998,"style":653},[652],[607,5000,5002,5005],{"className":5001},[657],[607,5003,781],{"className":5004},[657],[607,5006,5008],{"className":5007},[668],[607,5009,5011],{"className":5010},[672],[607,5012,5014],{"className":5013},[676],[607,5015,5017],{"className":5016,"style":653},[680],[607,5018,5019,5022],{"style":683},[607,5020],{"className":5021,"style":688},[687],[607,5023,5025],{"className":5024},[692,693,694,695],[607,5026,5028],{"className":5027},[657,695],[607,5029,4952],{"className":5030},[657,695],[607,5032],{"className":5033,"style":966},[965],[607,5035,4975],{"className":5036},[970],[607,5038],{"className":5039,"style":966},[965],[607,5041,5043,5047,5050,5058,5061,5064,5067],{"className":5042},[648],[607,5044],{"className":5045,"style":5046},[652],"height:0.8389em;vertical-align:-0.1944em;",[607,5048,3947],{"className":5049},[657],[607,5051,5053],{"className":5052},[657],[607,5054,5057],{"className":5055},[5056],"mpunct",",",[607,5059,2412],{"className":5060},[657],[607,5062],{"className":5063,"style":1081},[965],[607,5065,1645],{"className":5066},[1085],[607,5068],{"className":5069,"style":1081},[965],[607,5071,5073,5076,5079],{"className":5072},[648],[607,5074],{"className":5075,"style":653},[652],[607,5077,658],{"className":5078},[657],[607,5080,5082,5085],{"className":5081},[657],[607,5083,634],{"className":5084},[657],[607,5086,5088],{"className":5087},[668],[607,5089,5091],{"className":5090},[672],[607,5092,5094],{"className":5093},[676],[607,5095,5097],{"className":5096,"style":653},[680],[607,5098,5099,5102],{"style":683},[607,5100],{"className":5101,"style":688},[687],[607,5103,5105],{"className":5104},[692,693,694,695],[607,5106,1936],{"className":5107},[657,695],[1885,5109,5110],{},"environ 4 milliards",[598,5112,5113,5114,5142,5143,5274,5275,5278],{},"Inversement, pour écrire un entier ",[607,5115,5117,5130],{"className":5116},[610],[607,5118,5120],{"className":5119},[614],[616,5121,5122],{"xmlns":618},[620,5123,5124,5128],{},[623,5125,5126],{},[875,5127,1611],{},[636,5129,1611],{"encoding":638},[607,5131,5133],{"className":5132,"ariaHidden":644},[643],[607,5134,5136,5139],{"className":5135},[648],[607,5137],{"className":5138,"style":1664},[652],[607,5140,1611],{"className":5141,"style":1668},[657,893]," positif, il faut ",[607,5144,5146,5186],{"className":5145},[610],[607,5147,5149],{"className":5148},[614],[616,5150,5151],{"xmlns":618},[620,5152,5153,5183],{},[623,5154,5155,5158,5170,5172,5174,5176,5179,5181],{},[941,5156,5157],{"stretchy":1149},"⌊",[1152,5159,5160,5168],{},[623,5161,5162,5165],{},[875,5163,5164],{},"log",[941,5166,5167],{},"⁡",[629,5169,781],{},[941,5171,1150],{"stretchy":1149},[875,5173,1611],{},[941,5175,1197],{"stretchy":1149},[941,5177,5178],{"stretchy":1149},"⌋",[941,5180,2415],{},[629,5182,658],{},[636,5184,5185],{"encoding":638},"\\lfloor \\log_2(N) \\rfloor + 1",[607,5187,5189,5265],{"className":5188,"ariaHidden":644},[643],[607,5190,5192,5195,5198,5246,5249,5252,5256,5259,5262],{"className":5191},[648],[607,5193],{"className":5194,"style":1212},[652],[607,5196,5157],{"className":5197},[1216],[607,5199,5201,5209],{"className":5200},[1688],[607,5202,5204,5205],{"className":5203},[1688],"lo",[607,5206,5208],{"style":5207},"margin-right:0.0139em;","g",[607,5210,5212],{"className":5211},[668],[607,5213,5215,5237],{"className":5214},[672,1229],[607,5216,5218,5234],{"className":5217},[676],[607,5219,5222],{"className":5220,"style":5221},[680],"height:0.207em;",[607,5223,5225,5228],{"style":5224},"top:-2.4559em;margin-right:0.05em;",[607,5226],{"className":5227,"style":688},[687],[607,5229,5231],{"className":5230},[692,693,694,695],[607,5232,781],{"className":5233},[657,695],[607,5235,1262],{"className":5236},[1261],[607,5238,5240],{"className":5239},[676],[607,5241,5244],{"className":5242,"style":5243},[680],"height:0.2441em;",[607,5245],{},[607,5247,1150],{"className":5248},[1216],[607,5250,1611],{"className":5251,"style":1668},[657,893],[607,5253,5255],{"className":5254},[1416],")⌋",[607,5257],{"className":5258,"style":1081},[965],[607,5260,2415],{"className":5261},[1085],[607,5263],{"className":5264,"style":1081},[965],[607,5266,5268,5271],{"className":5267},[648],[607,5269],{"className":5270,"style":980},[652],[607,5272,658],{"className":5273},[657],"\nbits. En pratique, vous pouvez aussi compter en utilisant ",[1893,5276,5277],{},"bin(N)"," :",[2877,5280,5282],{"className":2879,"code":5281,"language":2881,"meta":2882,"style":2882},"n = 1000\nprint(bin(n))            # 0b1111101000\nprint(len(bin(n)) - 2)   # 10 — on retire le préfixe \"0b\"\n",[1893,5283,5284,5293,5308],{"__ignoreMap":2882},[607,5285,5286,5288,5290],{"class":2887,"line":2888},[607,5287,3718],{"class":2895},[607,5289,1614],{"class":3721},[607,5291,5292],{"class":2891}," 1000\n",[607,5294,5295,5297,5299,5302,5305],{"class":2887,"line":2918},[607,5296,2892],{"class":2891},[607,5298,1150],{"class":2895},[607,5300,5301],{"class":2891},"bin",[607,5303,5304],{"class":2895},"(n))            ",[607,5306,5307],{"class":2914},"# 0b1111101000\n",[607,5309,5310,5312,5314,5317,5319,5321,5324,5327,5330,5333],{"class":2887,"line":2942},[607,5311,2892],{"class":2891},[607,5313,1150],{"class":2895},[607,5315,5316],{"class":2891},"len",[607,5318,1150],{"class":2895},[607,5320,5301],{"class":2891},[607,5322,5323],{"class":2895},"(n)) ",[607,5325,5326],{"class":3721},"-",[607,5328,5329],{"class":2891}," 2",[607,5331,5332],{"class":2895},")   ",[607,5334,5335],{"class":2914},"# 10 — on retire le préfixe \"0b\"\n",[593,5337,5339],{"id":5338},"pièges-courants","Pièges courants",[5341,5342,5343],"warning",{},[3059,5344,5345,5465,5534],{},[3062,5346,5347,5348,5350,5351,5354,5355,5435,5436,5464],{},"Ne pas confondre la ",[602,5349,648],{}," et le ",[602,5352,5353],{},"nombre de chiffres",". ",[607,5356,5358,5380],{"className":5357},[610],[607,5359,5361],{"className":5360},[614],[616,5362,5363],{"xmlns":618},[620,5364,5365,5377],{},[623,5366,5367,5369,5371],{},[941,5368,1150],{"stretchy":1149},[629,5370,631],{},[1152,5372,5373,5375],{},[941,5374,1197],{"stretchy":1149},[629,5376,781],{},[636,5378,5379],{"encoding":638},"(10)_2",[607,5381,5383],{"className":5382,"ariaHidden":644},[643],[607,5384,5386,5389,5392,5395],{"className":5385},[648],[607,5387],{"className":5388,"style":1212},[652],[607,5390,1150],{"className":5391},[1216],[607,5393,631],{"className":5394},[657],[607,5396,5398,5401],{"className":5397},[1416],[607,5399,1197],{"className":5400},[1416],[607,5402,5404],{"className":5403},[668],[607,5405,5407,5427],{"className":5406},[672,1229],[607,5408,5410,5424],{"className":5409},[676],[607,5411,5413],{"className":5412,"style":1236},[680],[607,5414,5415,5418],{"style":1239},[607,5416],{"className":5417,"style":688},[687],[607,5419,5421],{"className":5420},[692,693,694,695],[607,5422,781],{"className":5423},[657,695],[607,5425,1262],{"className":5426},[1261],[607,5428,5430],{"className":5429},[676],[607,5431,5433],{"className":5432,"style":1370},[680],[607,5434],{}," vaut\n",[607,5437,5439,5452],{"className":5438},[610],[607,5440,5442],{"className":5441},[614],[616,5443,5444],{"xmlns":618},[620,5445,5446,5450],{},[623,5447,5448],{},[629,5449,781],{},[636,5451,781],{"encoding":638},[607,5453,5455],{"className":5454,"ariaHidden":644},[643],[607,5456,5458,5461],{"className":5457},[648],[607,5459],{"className":5460,"style":980},[652],[607,5462,781],{"className":5463},[657],", pas dix.",[3062,5466,5467,5468,5471,5472,5500,5501,5504,5505,5533],{},"En Python, ",[1893,5469,5470],{},"0b10"," est un entier dont la valeur est ",[607,5473,5475,5488],{"className":5474},[610],[607,5476,5478],{"className":5477},[614],[616,5479,5480],{"xmlns":618},[620,5481,5482,5486],{},[623,5483,5484],{},[629,5485,781],{},[636,5487,781],{"encoding":638},[607,5489,5491],{"className":5490,"ariaHidden":644},[643],[607,5492,5494,5497],{"className":5493},[648],[607,5495],{"className":5496,"style":980},[652],[607,5498,781],{"className":5499},[657],". Quand vous\nl'affichez avec ",[1893,5502,5503],{},"print(0b10)",", Python affiche ",[607,5506,5508,5521],{"className":5507},[610],[607,5509,5511],{"className":5510},[614],[616,5512,5513],{"xmlns":618},[620,5514,5515,5519],{},[623,5516,5517],{},[629,5518,781],{},[636,5520,781],{"encoding":638},[607,5522,5524],{"className":5523,"ariaHidden":644},[643],[607,5525,5527,5530],{"className":5526},[648],[607,5528],{"className":5529,"style":980},[652],[607,5531,781],{"className":5532},[657]," en décimal par défaut.",[3062,5535,5536,5537,5540,5541,5544],{},"L'écriture ",[1893,5538,5539],{},"010"," dans un code Python ancien (Python 2) était un octal —\nsource de bugs. En Python 3, il faut écrire ",[1893,5542,5543],{},"0o10"," explicitement.",[593,5546,5548],{"id":5547},"pour-aller-plus-loin","Pour aller plus loin",[598,5550,5551,5552,5555,5556,5618],{},"Python gère ",[602,5553,5554],{},"les entiers de taille arbitraire"," : vous pouvez calculer\n",[607,5557,5559,5577],{"className":5558},[610],[607,5560,5562],{"className":5561},[614],[616,5563,5564],{"xmlns":618},[620,5565,5566,5574],{},[623,5567,5568],{},[626,5569,5570,5572],{},[629,5571,781],{},[629,5573,3881],{},[636,5575,5576],{"encoding":638},"2^{1000}",[607,5578,5580],{"className":5579,"ariaHidden":644},[643],[607,5581,5583,5586],{"className":5582},[648],[607,5584],{"className":5585,"style":653},[652],[607,5587,5589,5592],{"className":5588},[657],[607,5590,781],{"className":5591},[657],[607,5593,5595],{"className":5594},[668],[607,5596,5598],{"className":5597},[672],[607,5599,5601],{"className":5600},[676],[607,5602,5604],{"className":5603,"style":653},[680],[607,5605,5606,5609],{"style":683},[607,5607],{"className":5608,"style":688},[687],[607,5610,5612],{"className":5611},[692,693,694,695],[607,5613,5615],{"className":5614},[657,695],[607,5616,3881],{"className":5617},[657,695]," sans erreur, contrairement à beaucoup d'autres langages où les\nentiers sont bornés à 32 ou 64 bits. Vous reverrez cette notion dans le cours\nsuivant sur les entiers relatifs.",[5620,5621,5622],"style",{},"html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}",{"title":2882,"searchDepth":2918,"depth":2918,"links":5624},[5625,5626,5628,5629,5630,5631,5632,5633],{"id":595,"depth":2918,"text":596},{"id":860,"depth":2918,"text":5627},"Le principe d'une base bbb",{"id":2284,"depth":2918,"text":2285},{"id":3074,"depth":2918,"text":3075},{"id":3835,"depth":2918,"text":3836},{"id":4343,"depth":2918,"text":4344},{"id":5338,"depth":2918,"text":5339},{"id":5547,"depth":2918,"text":5548},"Comment écrire un nombre en binaire, en hexadécimal ou en octal, et comment convertir d'une base à l'autre.",null,"md",{},true,[5640,5645],{"slug":2967,"kind":5641,"question":5642,"choices":5643,"correct":658,"multi":5644,"explanation":2882},"qcm","Que vaut (1101)2(1101)_2(1101)2​ en décimal ?",[2050,3066,3069,2016],false,{"slug":4234,"kind":5641,"question":5646,"choices":5647,"correct":781,"multi":5644,"explanation":2882},"Combien de bits sont nécessaires pour écrire (A3)16(A3)_{16}(A3)16​ ?",[3947,3207,1907,1944],{"title":263,"description":5634},"KHe64FYpinZWaTTv2GNqgCh3u5JXUV_9SiELR5sZQsM",{"id":5651,"title":5652,"bo":5653,"body":5654,"description":6786,"eval":5635,"extension":5636,"labo":5635,"meta":6787,"navigation":5644,"path":6788,"quizzes":6789,"readingTime":2888,"seo":6790,"stem":6791,"tp":5635,"__hash__":6792},"coursMemo\u002F1.nsi-1ere\u002Fpb-types-valeurs\u002F1.bases-entiers-positifs.memo.md","Bases de numération et entiers positifs — l'essentiel",[588],{"type":590,"value":5655,"toc":6779},[5656,5660,5723,5727,6213,6217,6471,6473,6688,6692,6776],[593,5657,5659],{"id":5658},"en-une-phrase","En une phrase",[598,5661,896,5662,5690,5691,5719,5720,2096],{},[607,5663,5665,5678],{"className":5664},[610],[607,5666,5668],{"className":5667},[614],[616,5669,5670],{"xmlns":618},[620,5671,5672,5676],{},[623,5673,5674],{},[875,5675,877],{},[636,5677,877],{"encoding":638},[607,5679,5681],{"className":5680,"ariaHidden":644},[643],[607,5682,5684,5687],{"className":5683},[648],[607,5685],{"className":5686,"style":889},[652],[607,5688,877],{"className":5689},[657,893],", chaque chiffre occupe une position qui correspond à une\npuissance de ",[607,5692,5694,5707],{"className":5693},[610],[607,5695,5697],{"className":5696},[614],[616,5698,5699],{"xmlns":618},[620,5700,5701,5705],{},[623,5702,5703],{},[875,5704,877],{},[636,5706,877],{"encoding":638},[607,5708,5710],{"className":5709,"ariaHidden":644},[643],[607,5711,5713,5716],{"className":5712},[648],[607,5714],{"className":5715,"style":889},[652],[607,5717,877],{"className":5718},[657,893]," — ",[602,5721,5722],{},"un nombre vaut la somme de ses chiffres pondérés par les\npuissances de la base",[593,5724,5726],{"id":5725},"à-mémoriser","À mémoriser",[3059,5728,5729,5739,5749,5764,6012,6210],{},[3062,5730,5731,5732,1895,5734,5736,5737,2096],{},"Base 2 : chiffres ",[1893,5733,634],{},[1893,5735,658],{},". Préfixe Python ",[1893,5738,1902],{},[3062,5740,5741,5742,1042,5744,5746,5747,2096],{},"Base 8 : chiffres ",[1893,5743,634],{},[1893,5745,1917],{},". Préfixe ",[1893,5748,1922],{},[3062,5750,5751,5752,1042,5754,5756,5757,5759,5760,5746,5762,2096],{},"Base 16 : chiffres ",[1893,5753,634],{},[1893,5755,1936],{}," puis ",[1893,5758,1957],{},"–",[1893,5761,1960],{},[1893,5763,1965],{},[3062,5765,5766,6011],{},[607,5767,5769,5820],{"className":5768},[610],[607,5770,5772],{"className":5771},[614],[616,5773,5774],{"xmlns":618},[620,5775,5776,5817],{},[623,5777,5778,5780,5782,5803,5809,5811],{},[875,5779,1611],{},[941,5781,1614],{},[5783,5784,5785,5787,5795],"msubsup",{},[941,5786,1620],{},[623,5788,5789,5791,5793],{},[875,5790,1503],{},[941,5792,1614],{},[629,5794,634],{},[623,5796,5797,5799,5801],{},[875,5798,1161],{},[941,5800,1059],{},[629,5802,658],{},[1152,5804,5805,5807],{},[875,5806,877],{},[875,5808,1503],{},[941,5810,1645],{},[626,5812,5813,5815],{},[875,5814,877],{},[875,5816,1503],{},[636,5818,5819],{"encoding":638},"N = \\sum_{i=0}^{n-1} b_i \\cdot b^i",[607,5821,5823,5841,5975],{"className":5822,"ariaHidden":644},[643],[607,5824,5826,5829,5832,5835,5838],{"className":5825},[648],[607,5827],{"className":5828,"style":1664},[652],[607,5830,1611],{"className":5831,"style":1668},[657,893],[607,5833],{"className":5834,"style":966},[965],[607,5836,1614],{"className":5837},[970],[607,5839],{"className":5840,"style":966},[965],[607,5842,5844,5848,5923,5926,5966,5969,5972],{"className":5843},[648],[607,5845],{"className":5846,"style":5847},[652],"height:1.2537em;vertical-align:-0.2997em;",[607,5849,5851,5856],{"className":5850},[1688],[607,5852,1620],{"className":5853,"style":5855},[1688,1733,5854],"small-op","position:relative;top:0em;",[607,5857,5859],{"className":5858},[668],[607,5860,5862,5914],{"className":5861},[672,1229],[607,5863,5865,5911],{"className":5864},[676],[607,5866,5869,5890],{"className":5867,"style":5868},[680],"height:0.954em;",[607,5870,5872,5875],{"style":5871},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[607,5873],{"className":5874,"style":688},[687],[607,5876,5878],{"className":5877},[692,693,694,695],[607,5879,5881,5884,5887],{"className":5880},[657,695],[607,5882,1503],{"className":5883},[657,893,695],[607,5885,1614],{"className":5886},[970,695],[607,5888,634],{"className":5889},[657,695],[607,5891,5893,5896],{"style":5892},"top:-3.2029em;margin-right:0.05em;",[607,5894],{"className":5895,"style":688},[687],[607,5897,5899],{"className":5898},[692,693,694,695],[607,5900,5902,5905,5908],{"className":5901},[657,695],[607,5903,1161],{"className":5904},[657,893,695],[607,5906,1059],{"className":5907},[1085,695],[607,5909,658],{"className":5910},[657,695],[607,5912,1262],{"className":5913},[1261],[607,5915,5917],{"className":5916},[676],[607,5918,5921],{"className":5919,"style":5920},[680],"height:0.2997em;",[607,5922],{},[607,5924],{"className":5925,"style":1324},[965],[607,5927,5929,5932],{"className":5928},[657],[607,5930,877],{"className":5931},[657,893],[607,5933,5935],{"className":5934},[668],[607,5936,5938,5958],{"className":5937},[672,1229],[607,5939,5941,5955],{"className":5940},[676],[607,5942,5944],{"className":5943,"style":1535},[680],[607,5945,5946,5949],{"style":1239},[607,5947],{"className":5948,"style":688},[687],[607,5950,5952],{"className":5951},[692,693,694,695],[607,5953,1503],{"className":5954},[657,893,695],[607,5956,1262],{"className":5957},[1261],[607,5959,5961],{"className":5960},[676],[607,5962,5964],{"className":5963,"style":1370},[680],[607,5965],{},[607,5967],{"className":5968,"style":1081},[965],[607,5970,1645],{"className":5971},[1085],[607,5973],{"className":5974,"style":1081},[965],[607,5976,5978,5982],{"className":5977},[648],[607,5979],{"className":5980,"style":5981},[652],"height:0.8247em;",[607,5983,5985,5988],{"className":5984},[657],[607,5986,877],{"className":5987},[657,893],[607,5989,5991],{"className":5990},[668],[607,5992,5994],{"className":5993},[672],[607,5995,5997],{"className":5996},[676],[607,5998,6000],{"className":5999,"style":5981},[680],[607,6001,6002,6005],{"style":683},[607,6003],{"className":6004,"style":688},[687],[607,6006,6008],{"className":6007},[692,693,694,695],[607,6009,1503],{"className":6010},[657,893,695]," — formule de conversion vers le décimal.",[3062,6013,4347,6014,6042,6043,6101,6102,1042,6130,2096],{},[607,6015,6017,6030],{"className":6016},[610],[607,6018,6020],{"className":6019},[614],[616,6021,6022],{"xmlns":618},[620,6023,6024,6028],{},[623,6025,6026],{},[875,6027,1161],{},[636,6029,1161],{"encoding":638},[607,6031,6033],{"className":6032,"ariaHidden":644},[643],[607,6034,6036,6039],{"className":6035},[648],[607,6037],{"className":6038,"style":4373},[652],[607,6040,1161],{"className":6041},[657,893]," bits, on code ",[607,6044,6046,6063],{"className":6045},[610],[607,6047,6049],{"className":6048},[614],[616,6050,6051],{"xmlns":618},[620,6052,6053,6061],{},[623,6054,6055],{},[626,6056,6057,6059],{},[629,6058,781],{},[875,6060,1161],{},[636,6062,4398],{"encoding":638},[607,6064,6066],{"className":6065,"ariaHidden":644},[643],[607,6067,6069,6072],{"className":6068},[648],[607,6070],{"className":6071,"style":4408},[652],[607,6073,6075,6078],{"className":6074},[657],[607,6076,781],{"className":6077},[657],[607,6079,6081],{"className":6080},[668],[607,6082,6084],{"className":6083},[672],[607,6085,6087],{"className":6086},[676],[607,6088,6090],{"className":6089,"style":4408},[680],[607,6091,6092,6095],{"style":683},[607,6093],{"className":6094,"style":688},[687],[607,6096,6098],{"className":6097},[692,693,694,695],[607,6099,1161],{"className":6100},[657,893,695]," valeurs, de ",[607,6103,6105,6118],{"className":6104},[610],[607,6106,6108],{"className":6107},[614],[616,6109,6110],{"xmlns":618},[620,6111,6112,6116],{},[623,6113,6114],{},[629,6115,634],{},[636,6117,634],{"encoding":638},[607,6119,6121],{"className":6120,"ariaHidden":644},[643],[607,6122,6124,6127],{"className":6123},[648],[607,6125],{"className":6126,"style":980},[652],[607,6128,634],{"className":6129},[657],[607,6131,6133,6154],{"className":6132},[610],[607,6134,6136],{"className":6135},[614],[616,6137,6138],{"xmlns":618},[620,6139,6140,6152],{},[623,6141,6142,6148,6150],{},[626,6143,6144,6146],{},[629,6145,781],{},[875,6147,1161],{},[941,6149,1059],{},[629,6151,658],{},[636,6153,4491],{"encoding":638},[607,6155,6157,6201],{"className":6156,"ariaHidden":644},[643],[607,6158,6160,6163,6192,6195,6198],{"className":6159},[648],[607,6161],{"className":6162,"style":4501},[652],[607,6164,6166,6169],{"className":6165},[657],[607,6167,781],{"className":6168},[657],[607,6170,6172],{"className":6171},[668],[607,6173,6175],{"className":6174},[672],[607,6176,6178],{"className":6177},[676],[607,6179,6181],{"className":6180,"style":4408},[680],[607,6182,6183,6186],{"style":683},[607,6184],{"className":6185,"style":688},[687],[607,6187,6189],{"className":6188},[692,693,694,695],[607,6190,1161],{"className":6191},[657,893,695],[607,6193],{"className":6194,"style":1081},[965],[607,6196,1059],{"className":6197},[1085],[607,6199],{"className":6200,"style":1081},[965],[607,6202,6204,6207],{"className":6203},[648],[607,6205],{"className":6206,"style":980},[652],[607,6208,658],{"className":6209},[657],[3062,6211,6212],{},"1 chiffre hexadécimal = 4 bits exactement.",[593,6214,6216],{"id":6215},"à-savoir-reconnaître","À savoir reconnaître",[1858,6218,6219,6229],{},[1861,6220,6221],{},[1864,6222,6223,6226],{},[1867,6224,6225],{},"Situation",[1867,6227,6228],{},"Action à mener",[1880,6230,6231,6299,6307,6315],{},[1864,6232,6233,6236],{},[1885,6234,6235],{},"Convertir binaire → décimal",[1885,6237,6238,6239,6298],{},"Somme des ",[607,6240,6242,6260],{"className":6241},[610],[607,6243,6245],{"className":6244},[614],[616,6246,6247],{"xmlns":618},[620,6248,6249,6257],{},[623,6250,6251],{},[626,6252,6253,6255],{},[629,6254,781],{},[875,6256,1503],{},[636,6258,6259],{"encoding":638},"2^i",[607,6261,6263],{"className":6262,"ariaHidden":644},[643],[607,6264,6266,6269],{"className":6265},[648],[607,6267],{"className":6268,"style":5981},[652],[607,6270,6272,6275],{"className":6271},[657],[607,6273,781],{"className":6274},[657],[607,6276,6278],{"className":6277},[668],[607,6279,6281],{"className":6280},[672],[607,6282,6284],{"className":6283},[676],[607,6285,6287],{"className":6286,"style":5981},[680],[607,6288,6289,6292],{"style":683},[607,6290],{"className":6291,"style":688},[687],[607,6293,6295],{"className":6294},[692,693,694,695],[607,6296,1503],{"className":6297},[657,893,695]," pour les bits à 1.",[1864,6300,6301,6304],{},[1885,6302,6303],{},"Convertir décimal → binaire",[1885,6305,6306],{},"Divisions successives par 2, lecture des restes de bas en haut.",[1864,6308,6309,6312],{},[1885,6310,6311],{},"Convertir binaire ↔ hexa",[1885,6313,6314],{},"Regrouper par paquets de 4 bits, ou utiliser le tableau de correspondance.",[1864,6316,6317,6348],{},[1885,6318,6319,6320],{},"Compter le nombre de bits d'un entier ",[607,6321,6323,6336],{"className":6322},[610],[607,6324,6326],{"className":6325},[614],[616,6327,6328],{"xmlns":618},[620,6329,6330,6334],{},[623,6331,6332],{},[875,6333,1611],{},[636,6335,1611],{"encoding":638},[607,6337,6339],{"className":6338,"ariaHidden":644},[643],[607,6340,6342,6345],{"className":6341},[648],[607,6343],{"className":6344,"style":1664},[652],[607,6346,1611],{"className":6347,"style":1668},[657,893],[1885,6349,6350,6466,6467,6470],{},[607,6351,6353,6385],{"className":6352},[610],[607,6354,6356],{"className":6355},[614],[616,6357,6358],{"xmlns":618},[620,6359,6360,6382],{},[623,6361,6362,6364,6374,6376,6378,6380],{},[941,6363,5157],{"stretchy":1149},[1152,6365,6366,6372],{},[623,6367,6368,6370],{},[875,6369,5164],{},[941,6371,5167],{},[629,6373,781],{},[875,6375,1611],{},[941,6377,5178],{"stretchy":1149},[941,6379,2415],{},[629,6381,658],{},[636,6383,6384],{"encoding":638},"\\lfloor \\log_2 N \\rfloor + 1",[607,6386,6388,6457],{"className":6387,"ariaHidden":644},[643],[607,6389,6391,6394,6397,6439,6442,6445,6448,6451,6454],{"className":6390},[648],[607,6392],{"className":6393,"style":1212},[652],[607,6395,5157],{"className":6396},[1216],[607,6398,6400,6405],{"className":6399},[1688],[607,6401,5204,6403],{"className":6402},[1688],[607,6404,5208],{"style":5207},[607,6406,6408],{"className":6407},[668],[607,6409,6411,6431],{"className":6410},[672,1229],[607,6412,6414,6428],{"className":6413},[676],[607,6415,6417],{"className":6416,"style":5221},[680],[607,6418,6419,6422],{"style":5224},[607,6420],{"className":6421,"style":688},[687],[607,6423,6425],{"className":6424},[692,693,694,695],[607,6426,781],{"className":6427},[657,695],[607,6429,1262],{"className":6430},[1261],[607,6432,6434],{"className":6433},[676],[607,6435,6437],{"className":6436,"style":5243},[680],[607,6438],{},[607,6440],{"className":6441,"style":1324},[965],[607,6443,1611],{"className":6444,"style":1668},[657,893],[607,6446,5178],{"className":6447},[1416],[607,6449],{"className":6450,"style":1081},[965],[607,6452,2415],{"className":6453},[1085],[607,6455],{"className":6456,"style":1081},[965],[607,6458,6460,6463],{"className":6459},[648],[607,6461],{"className":6462,"style":980},[652],[607,6464,658],{"className":6465},[657],", ou ",[1893,6468,6469],{},"len(bin(N)) - 2"," en Python.",[593,6472,5339],{"id":5338},[3059,6474,6475,6567,6685],{},[3062,6476,6477,2035,6479,6507,6508,5719,6536,6538,6539,2096],{},[1893,6478,5470],{},[607,6480,6482,6495],{"className":6481},[610],[607,6483,6485],{"className":6484},[614],[616,6486,6487],{"xmlns":618},[620,6488,6489,6493],{},[623,6490,6491],{},[629,6492,781],{},[636,6494,781],{"encoding":638},[607,6496,6498],{"className":6497,"ariaHidden":644},[643],[607,6499,6501,6504],{"className":6500},[648],[607,6502],{"className":6503,"style":980},[652],[607,6505,781],{"className":6506},[657],", pas ",[607,6509,6511,6524],{"className":6510},[610],[607,6512,6514],{"className":6513},[614],[616,6515,6516],{"xmlns":618},[620,6517,6518,6522],{},[623,6519,6520],{},[629,6521,631],{},[636,6523,631],{"encoding":638},[607,6525,6527],{"className":6526,"ariaHidden":644},[643],[607,6528,6530,6533],{"className":6529},[648],[607,6531],{"className":6532,"style":980},[652],[607,6534,631],{"className":6535},[657],[1893,6537,5503],{}," affiche ",[607,6540,6542,6555],{"className":6541},[610],[607,6543,6545],{"className":6544},[614],[616,6546,6547],{"xmlns":618},[620,6548,6549,6553],{},[623,6550,6551],{},[629,6552,781],{},[636,6554,781],{"encoding":638},[607,6556,6558],{"className":6557,"ariaHidden":644},[643],[607,6559,6561,6564],{"className":6560},[648],[607,6562],{"className":6563,"style":980},[652],[607,6565,781],{"className":6566},[657],[3062,6568,6569,6570,2065,6572,6575,6576,6656,6657,2096],{},"Ne pas confondre ",[602,6571,648],{},[602,6573,6574],{},"chiffre"," : ",[607,6577,6579,6601],{"className":6578},[610],[607,6580,6582],{"className":6581},[614],[616,6583,6584],{"xmlns":618},[620,6585,6586,6598],{},[623,6587,6588,6590,6592],{},[941,6589,1150],{"stretchy":1149},[629,6591,631],{},[1152,6593,6594,6596],{},[941,6595,1197],{"stretchy":1149},[875,6597,877],{},[636,6599,6600],{"encoding":638},"(10)_b",[607,6602,6604],{"className":6603,"ariaHidden":644},[643],[607,6605,6607,6610,6613,6616],{"className":6606},[648],[607,6608],{"className":6609,"style":1212},[652],[607,6611,1150],{"className":6612},[1216],[607,6614,631],{"className":6615},[657],[607,6617,6619,6622],{"className":6618},[1416],[607,6620,1197],{"className":6621},[1416],[607,6623,6625],{"className":6624},[668],[607,6626,6628,6648],{"className":6627},[672,1229],[607,6629,6631,6645],{"className":6630},[676],[607,6632,6634],{"className":6633,"style":1432},[680],[607,6635,6636,6639],{"style":1239},[607,6637],{"className":6638,"style":688},[687],[607,6640,6642],{"className":6641},[692,693,694,695],[607,6643,877],{"className":6644},[657,893,695],[607,6646,1262],{"className":6647},[1261],[607,6649,6651],{"className":6650},[676],[607,6652,6654],{"className":6653,"style":1370},[680],[607,6655],{}," vaut toujours ",[607,6658,6660,6673],{"className":6659},[610],[607,6661,6663],{"className":6662},[614],[616,6664,6665],{"xmlns":618},[620,6666,6667,6671],{},[623,6668,6669],{},[875,6670,877],{},[636,6672,877],{"encoding":638},[607,6674,6676],{"className":6675,"ariaHidden":644},[643],[607,6677,6679,6682],{"className":6678},[648],[607,6680],{"className":6681,"style":889},[652],[607,6683,877],{"className":6684},[657,893],[3062,6686,6687],{},"En binaire, on lit de la droite (poids faible) vers la gauche (poids fort).",[593,6689,6691],{"id":6690},"syntaxe-python","Syntaxe Python",[2877,6693,6695],{"className":2879,"code":6694,"language":2881,"meta":2882,"style":2882},"int(\"1011\", 2)   # 11\nint(\"2F\", 16)    # 47\nbin(13)          # '0b1101'\nhex(255)         # '0xff'\noct(15)          # '0o17'\n",[1893,6696,6697,6713,6732,6746,6761],{"__ignoreMap":2882},[607,6698,6699,6701,6703,6705,6707,6709,6711],{"class":2887,"line":2888},[607,6700,2898],{"class":2891},[607,6702,1150],{"class":2895},[607,6704,2904],{"class":2903},[607,6706,1895],{"class":2895},[607,6708,781],{"class":2891},[607,6710,5332],{"class":2895},[607,6712,2915],{"class":2914},[607,6714,6715,6717,6719,6722,6724,6726,6729],{"class":2887,"line":2918},[607,6716,2898],{"class":2891},[607,6718,1150],{"class":2895},[607,6720,6721],{"class":2903},"\"2F\"",[607,6723,1895],{"class":2895},[607,6725,1944],{"class":2891},[607,6727,6728],{"class":2895},")    ",[607,6730,6731],{"class":2914},"# 47\n",[607,6733,6734,6736,6738,6740,6743],{"class":2887,"line":2942},[607,6735,5301],{"class":2891},[607,6737,1150],{"class":2895},[607,6739,3066],{"class":2891},[607,6741,6742],{"class":2895},")          ",[607,6744,6745],{"class":2914},"# '0b1101'\n",[607,6747,6748,6751,6753,6755,6758],{"class":2887,"line":3793},[607,6749,6750],{"class":2891},"hex",[607,6752,1150],{"class":2895},[607,6754,4788],{"class":2891},[607,6756,6757],{"class":2895},")         ",[607,6759,6760],{"class":2914},"# '0xff'\n",[607,6762,6764,6767,6769,6771,6773],{"class":2887,"line":6763},5,[607,6765,6766],{"class":2891},"oct",[607,6768,1150],{"class":2895},[607,6770,2016],{"class":2891},[607,6772,6742],{"class":2895},[607,6774,6775],{"class":2914},"# '0o17'\n",[5620,6777,6778],{},"html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":2882,"searchDepth":2918,"depth":2918,"links":6780},[6781,6782,6783,6784,6785],{"id":5658,"depth":2918,"text":5659},{"id":5725,"depth":2918,"text":5726},{"id":6215,"depth":2918,"text":6216},{"id":5338,"depth":2918,"text":5339},{"id":6690,"depth":2918,"text":6691},"Mémo de révision sur les bases binaire, hexadécimale, octale et leurs conversions.",{},"\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fbases-entiers-positifs.memo",[],{"title":5652,"description":6786},"1.nsi-1ere\u002Fpb-types-valeurs\u002F1.bases-entiers-positifs.memo","cEzQeAoR_6g9f16k8fHg3RCQc91qV69ioPQoBdqd_V8",{"id":6794,"title":6795,"body":6796,"description":8213,"extension":5636,"meta":8214,"navigation":5644,"path":8215,"seo":8216,"stem":8217,"__hash__":8218},"coursSlides\u002F1.nsi-1ere\u002Fpb-types-valeurs\u002F1.bases-entiers-positifs.slides.md","Bases de numération et entiers positifs — diapositives",{"type":590,"value":6797,"toc":8211},[6798,6803,6806,6809,6813,6832,6834,6866,7108,7111,7113,7117,7397,7399,7403,7443,7549,7551,7555,7558,7752,7754,7757,7802,7804,7836,7975,8007,8009,8013,8209],[6799,6800,6802],"h1",{"id":6801},"bases-de-numération","Bases de numération",[598,6804,6805],{},"Représenter un entier positif en base 2, 8, 10, 16.",[6807,6808],"hr",{},[6799,6810,6812],{"id":6811},"pourquoi-plusieurs-bases","Pourquoi plusieurs bases ?",[3059,6814,6815,6820,6826],{},[3062,6816,6817,6818,2096],{},"Une machine ne distingue que 2 états : ",[602,6819,1889],{},[3062,6821,6822,6823,6825],{},"Le binaire est illisible pour l'humain — d'où l'",[602,6824,1947],{}," (4 bits par chiffre).",[3062,6827,6828,6829,6831],{},"L'",[602,6830,1910],{}," est plus rare aujourd'hui mais apparaît encore (permissions Unix).",[6807,6833],{},[6799,6835,6837,6838],{"id":6836},"principe-dune-base-bbb","Principe d'une base ",[607,6839,6841,6854],{"className":6840},[610],[607,6842,6844],{"className":6843},[614],[616,6845,6846],{"xmlns":618},[620,6847,6848,6852],{},[623,6849,6850],{},[875,6851,877],{},[636,6853,877],{"encoding":638},[607,6855,6857],{"className":6856,"ariaHidden":644},[643],[607,6858,6860,6863],{"className":6859},[648],[607,6861],{"className":6862,"style":889},[652],[607,6864,877],{"className":6865},[657,893],[607,6867,6869],{"className":6868},[1595],[607,6870,6872,6921],{"className":6871},[610],[607,6873,6875],{"className":6874},[614],[616,6876,6877],{"xmlns":618,"display":1604},[620,6878,6879,6919],{},[623,6880,6881,6883,6885,6905,6911,6913],{},[875,6882,1611],{},[941,6884,1614],{},[1616,6886,6887,6889,6897],{},[941,6888,1620],{},[623,6890,6891,6893,6895],{},[875,6892,1503],{},[941,6894,1614],{},[629,6896,634],{},[623,6898,6899,6901,6903],{},[875,6900,1161],{},[941,6902,1059],{},[629,6904,658],{},[1152,6906,6907,6909],{},[875,6908,877],{},[875,6910,1503],{},[941,6912,1645],{},[626,6914,6915,6917],{},[875,6916,877],{},[875,6918,1503],{},[636,6920,5819],{"encoding":638},[607,6922,6924,6942,7073],{"className":6923,"ariaHidden":644},[643],[607,6925,6927,6930,6933,6936,6939],{"className":6926},[648],[607,6928],{"className":6929,"style":1664},[652],[607,6931,1611],{"className":6932,"style":1668},[657,893],[607,6934],{"className":6935,"style":966},[965],[607,6937,1614],{"className":6938},[970],[607,6940],{"className":6941,"style":966},[965],[607,6943,6945,6948,7021,7024,7064,7067,7070],{"className":6944},[648],[607,6946],{"className":6947,"style":1684},[652],[607,6949,6951],{"className":6950},[1688,1689],[607,6952,6954,7013],{"className":6953},[672,1229],[607,6955,6957,7010],{"className":6956},[676],[607,6958,6960,6980,6990],{"className":6959,"style":1699},[680],[607,6961,6962,6965],{"style":1702},[607,6963],{"className":6964,"style":1706},[687],[607,6966,6968],{"className":6967},[692,693,694,695],[607,6969,6971,6974,6977],{"className":6970},[657,695],[607,6972,1503],{"className":6973},[657,893,695],[607,6975,1614],{"className":6976},[970,695],[607,6978,634],{"className":6979},[657,695],[607,6981,6982,6985],{"style":1724},[607,6983],{"className":6984,"style":1706},[687],[607,6986,6987],{},[607,6988,1620],{"className":6989},[1688,1733,1734],[607,6991,6992,6995],{"style":1737},[607,6993],{"className":6994,"style":1706},[687],[607,6996,6998],{"className":6997},[692,693,694,695],[607,6999,7001,7004,7007],{"className":7000},[657,695],[607,7002,1161],{"className":7003},[657,893,695],[607,7005,1059],{"className":7006},[1085,695],[607,7008,658],{"className":7009},[657,695],[607,7011,1262],{"className":7012},[1261],[607,7014,7016],{"className":7015},[676],[607,7017,7019],{"className":7018,"style":1765},[680],[607,7020],{},[607,7022],{"className":7023,"style":1324},[965],[607,7025,7027,7030],{"className":7026},[657],[607,7028,877],{"className":7029},[657,893],[607,7031,7033],{"className":7032},[668],[607,7034,7036,7056],{"className":7035},[672,1229],[607,7037,7039,7053],{"className":7038},[676],[607,7040,7042],{"className":7041,"style":1535},[680],[607,7043,7044,7047],{"style":1239},[607,7045],{"className":7046,"style":688},[687],[607,7048,7050],{"className":7049},[692,693,694,695],[607,7051,1503],{"className":7052},[657,893,695],[607,7054,1262],{"className":7055},[1261],[607,7057,7059],{"className":7058},[676],[607,7060,7062],{"className":7061,"style":1370},[680],[607,7063],{},[607,7065],{"className":7066,"style":1081},[965],[607,7068,1645],{"className":7069},[1085],[607,7071],{"className":7072,"style":1081},[965],[607,7074,7076,7079],{"className":7075},[648],[607,7077],{"className":7078,"style":1826},[652],[607,7080,7082,7085],{"className":7081},[657],[607,7083,877],{"className":7084},[657,893],[607,7086,7088],{"className":7087},[668],[607,7089,7091],{"className":7090},[672],[607,7092,7094],{"className":7093},[676],[607,7095,7097],{"className":7096,"style":1826},[680],[607,7098,7099,7102],{"style":1847},[607,7100],{"className":7101,"style":688},[687],[607,7103,7105],{"className":7104},[692,693,694,695],[607,7106,1503],{"className":7107},[657,893,695],[598,7109,7110],{},"Chaque position d'un chiffre correspond à une puissance de la base.",[6807,7112],{},[6799,7114,7116],{"id":7115},"exemple-binaire-vers-décimal","Exemple — binaire vers décimal",[598,7118,7119],{},[607,7120,7122,7180],{"className":7121},[610],[607,7123,7125],{"className":7124},[614],[616,7126,7127],{"xmlns":618},[620,7128,7129,7177],{},[623,7130,7131,7133,7135,7141,7143,7145,7147,7149,7151,7153,7155,7157,7159,7161,7163,7165,7167,7169,7171,7173,7175],{},[941,7132,1150],{"stretchy":1149},[629,7134,2119],{},[1152,7136,7137,7139],{},[941,7138,1197],{"stretchy":1149},[629,7140,781],{},[941,7142,1614],{},[629,7144,658],{},[941,7146,1645],{},[629,7148,1907],{},[941,7150,2415],{},[629,7152,634],{},[941,7154,1645],{},[629,7156,3947],{},[941,7158,2415],{},[629,7160,658],{},[941,7162,1645],{},[629,7164,781],{},[941,7166,2415],{},[629,7168,658],{},[941,7170,1645],{},[629,7172,658],{},[941,7174,1614],{},[629,7176,2050],{},[636,7178,7179],{"encoding":638},"(1011)_2 = 1 \\cdot 8 + 0 \\cdot 4 + 1 \\cdot 2 + 1 \\cdot 1 = 11",[607,7181,7183,7244,7262,7280,7298,7316,7334,7352,7370,7388],{"className":7182,"ariaHidden":644},[643],[607,7184,7186,7189,7192,7195,7235,7238,7241],{"className":7185},[648],[607,7187],{"className":7188,"style":1212},[652],[607,7190,1150],{"className":7191},[1216],[607,7193,2119],{"className":7194},[657],[607,7196,7198,7201],{"className":7197},[1416],[607,7199,1197],{"className":7200},[1416],[607,7202,7204],{"className":7203},[668],[607,7205,7207,7227],{"className":7206},[672,1229],[607,7208,7210,7224],{"className":7209},[676],[607,7211,7213],{"className":7212,"style":1236},[680],[607,7214,7215,7218],{"style":1239},[607,7216],{"className":7217,"style":688},[687],[607,7219,7221],{"className":7220},[692,693,694,695],[607,7222,781],{"className":7223},[657,695],[607,7225,1262],{"className":7226},[1261],[607,7228,7230],{"className":7229},[676],[607,7231,7233],{"className":7232,"style":1370},[680],[607,7234],{},[607,7236],{"className":7237,"style":966},[965],[607,7239,1614],{"className":7240},[970],[607,7242],{"className":7243,"style":966},[965],[607,7245,7247,7250,7253,7256,7259],{"className":7246},[648],[607,7248],{"className":7249,"style":980},[652],[607,7251,658],{"className":7252},[657],[607,7254],{"className":7255,"style":1081},[965],[607,7257,1645],{"className":7258},[1085],[607,7260],{"className":7261,"style":1081},[965],[607,7263,7265,7268,7271,7274,7277],{"className":7264},[648],[607,7266],{"className":7267,"style":2793},[652],[607,7269,1907],{"className":7270},[657],[607,7272],{"className":7273,"style":1081},[965],[607,7275,2415],{"className":7276},[1085],[607,7278],{"className":7279,"style":1081},[965],[607,7281,7283,7286,7289,7292,7295],{"className":7282},[648],[607,7284],{"className":7285,"style":980},[652],[607,7287,634],{"className":7288},[657],[607,7290],{"className":7291,"style":1081},[965],[607,7293,1645],{"className":7294},[1085],[607,7296],{"className":7297,"style":1081},[965],[607,7299,7301,7304,7307,7310,7313],{"className":7300},[648],[607,7302],{"className":7303,"style":2793},[652],[607,7305,3947],{"className":7306},[657],[607,7308],{"className":7309,"style":1081},[965],[607,7311,2415],{"className":7312},[1085],[607,7314],{"className":7315,"style":1081},[965],[607,7317,7319,7322,7325,7328,7331],{"className":7318},[648],[607,7320],{"className":7321,"style":980},[652],[607,7323,658],{"className":7324},[657],[607,7326],{"className":7327,"style":1081},[965],[607,7329,1645],{"className":7330},[1085],[607,7332],{"className":7333,"style":1081},[965],[607,7335,7337,7340,7343,7346,7349],{"className":7336},[648],[607,7338],{"className":7339,"style":2793},[652],[607,7341,781],{"className":7342},[657],[607,7344],{"className":7345,"style":1081},[965],[607,7347,2415],{"className":7348},[1085],[607,7350],{"className":7351,"style":1081},[965],[607,7353,7355,7358,7361,7364,7367],{"className":7354},[648],[607,7356],{"className":7357,"style":980},[652],[607,7359,658],{"className":7360},[657],[607,7362],{"className":7363,"style":1081},[965],[607,7365,1645],{"className":7366},[1085],[607,7368],{"className":7369,"style":1081},[965],[607,7371,7373,7376,7379,7382,7385],{"className":7372},[648],[607,7374],{"className":7375,"style":980},[652],[607,7377,658],{"className":7378},[657],[607,7380],{"className":7381,"style":966},[965],[607,7383,1614],{"className":7384},[970],[607,7386],{"className":7387,"style":966},[965],[607,7389,7391,7394],{"className":7390},[648],[607,7392],{"className":7393,"style":980},[652],[607,7395,2050],{"className":7396},[657],[6807,7398],{},[6799,7400,7402],{"id":7401},"décimal-vers-binaire-divisions-successives","Décimal vers binaire — divisions successives",[1858,7404,7405,7413],{},[1861,7406,7407],{},[1864,7408,7409,7411],{},[1867,7410,3126],{},[1867,7412,3132],{},[1880,7414,7415,7422,7429,7436],{},[1864,7416,7417,7420],{},[1885,7418,7419],{},"13 \u002F 2 = 6",[1885,7421,658],{},[1864,7423,7424,7427],{},[1885,7425,7426],{},"6 \u002F 2 = 3",[1885,7428,634],{},[1864,7430,7431,7434],{},[1885,7432,7433],{},"3 \u002F 2 = 1",[1885,7435,658],{},[1864,7437,7438,7441],{},[1885,7439,7440],{},"1 \u002F 2 = 0",[1885,7442,658],{},[598,7444,7445,7446,6575,7448,2096],{},"Lecture ",[602,7447,3085],{},[607,7449,7451,7476],{"className":7450},[610],[607,7452,7454],{"className":7453},[614],[616,7455,7456],{"xmlns":618},[620,7457,7458,7474],{},[623,7459,7460,7462,7464,7466,7468],{},[629,7461,3066],{},[941,7463,1614],{},[941,7465,1150],{"stretchy":1149},[629,7467,2990],{},[1152,7469,7470,7472],{},[941,7471,1197],{"stretchy":1149},[629,7473,781],{},[636,7475,3632],{"encoding":638},[607,7477,7479,7497],{"className":7478,"ariaHidden":644},[643],[607,7480,7482,7485,7488,7491,7494],{"className":7481},[648],[607,7483],{"className":7484,"style":980},[652],[607,7486,3066],{"className":7487},[657],[607,7489],{"className":7490,"style":966},[965],[607,7492,1614],{"className":7493},[970],[607,7495],{"className":7496,"style":966},[965],[607,7498,7500,7503,7506,7509],{"className":7499},[648],[607,7501],{"className":7502,"style":1212},[652],[607,7504,1150],{"className":7505},[1216],[607,7507,2990],{"className":7508},[657],[607,7510,7512,7515],{"className":7511},[1416],[607,7513,1197],{"className":7514},[1416],[607,7516,7518],{"className":7517},[668],[607,7519,7521,7541],{"className":7520},[672,1229],[607,7522,7524,7538],{"className":7523},[676],[607,7525,7527],{"className":7526,"style":1236},[680],[607,7528,7529,7532],{"style":1239},[607,7530],{"className":7531,"style":688},[687],[607,7533,7535],{"className":7534},[692,693,694,695],[607,7536,781],{"className":7537},[657,695],[607,7539,1262],{"className":7540},[1261],[607,7542,7544],{"className":7543},[676],[607,7545,7547],{"className":7546,"style":1370},[680],[607,7548],{},[6807,7550],{},[6799,7552,7554],{"id":7553},"le-pont-binaire-hexadécimal","Le pont binaire — hexadécimal",[598,7556,7557],{},"1 chiffre hexadécimal = 4 bits.",[598,7559,7560],{},[607,7561,7563,7606],{"className":7562},[610],[607,7564,7566],{"className":7565},[614],[616,7567,7568],{"xmlns":618},[620,7569,7570,7604],{},[623,7571,7572,7574,7576,7578,7584,7586,7588,7590,7592,7594,7600,7602],{},[941,7573,1150],{"stretchy":1149},[629,7575,781],{},[875,7577,1960],{},[1152,7579,7580,7582],{},[941,7581,1197],{"stretchy":1149},[629,7583,1944],{},[941,7585,1614],{},[941,7587,1150],{"stretchy":1149},[629,7589,3912],{},[4059,7591,4061],{},[629,7593,4024],{},[1152,7595,7596,7598],{},[941,7597,1197],{"stretchy":1149},[629,7599,781],{},[941,7601,1614],{},[629,7603,4074],{},[636,7605,4077],{"encoding":638},[607,7607,7609,7676,7743],{"className":7608,"ariaHidden":644},[643],[607,7610,7612,7615,7618,7621,7624,7667,7670,7673],{"className":7611},[648],[607,7613],{"className":7614,"style":1212},[652],[607,7616,1150],{"className":7617},[1216],[607,7619,781],{"className":7620},[657],[607,7622,1960],{"className":7623,"style":4096},[657,893],[607,7625,7627,7630],{"className":7626},[1416],[607,7628,1197],{"className":7629},[1416],[607,7631,7633],{"className":7632},[668],[607,7634,7636,7659],{"className":7635},[672,1229],[607,7637,7639,7656],{"className":7638},[676],[607,7640,7642],{"className":7641,"style":1236},[680],[607,7643,7644,7647],{"style":1239},[607,7645],{"className":7646,"style":688},[687],[607,7648,7650],{"className":7649},[692,693,694,695],[607,7651,7653],{"className":7652},[657,695],[607,7654,1944],{"className":7655},[657,695],[607,7657,1262],{"className":7658},[1261],[607,7660,7662],{"className":7661},[676],[607,7663,7665],{"className":7664,"style":1370},[680],[607,7666],{},[607,7668],{"className":7669,"style":966},[965],[607,7671,1614],{"className":7672},[970],[607,7674],{"className":7675,"style":966},[965],[607,7677,7679,7682,7685,7688,7691,7694,7734,7737,7740],{"className":7678},[648],[607,7680],{"className":7681,"style":1212},[652],[607,7683,1150],{"className":7684},[1216],[607,7686,3912],{"className":7687},[657],[607,7689,4061],{"className":7690},[965],[607,7692,4024],{"className":7693},[657],[607,7695,7697,7700],{"className":7696},[1416],[607,7698,1197],{"className":7699},[1416],[607,7701,7703],{"className":7702},[668],[607,7704,7706,7726],{"className":7705},[672,1229],[607,7707,7709,7723],{"className":7708},[676],[607,7710,7712],{"className":7711,"style":1236},[680],[607,7713,7714,7717],{"style":1239},[607,7715],{"className":7716,"style":688},[687],[607,7718,7720],{"className":7719},[692,693,694,695],[607,7721,781],{"className":7722},[657,695],[607,7724,1262],{"className":7725},[1261],[607,7727,7729],{"className":7728},[676],[607,7730,7732],{"className":7731,"style":1370},[680],[607,7733],{},[607,7735],{"className":7736,"style":966},[965],[607,7738,1614],{"className":7739},[970],[607,7741],{"className":7742,"style":966},[965],[607,7744,7746,7749],{"className":7745},[648],[607,7747],{"className":7748,"style":980},[652],[607,7750,4074],{"className":7751},[657],[6807,7753],{},[6799,7755,7756],{"id":2881},"Python",[2877,7758,7760],{"className":2879,"code":7759,"language":2881,"meta":2882,"style":2882},"int(\"1011\", 2)   # 11\nbin(13)          # '0b1101'\nhex(255)         # '0xff'\n",[1893,7761,7762,7778,7790],{"__ignoreMap":2882},[607,7763,7764,7766,7768,7770,7772,7774,7776],{"class":2887,"line":2888},[607,7765,2898],{"class":2891},[607,7767,1150],{"class":2895},[607,7769,2904],{"class":2903},[607,7771,1895],{"class":2895},[607,7773,781],{"class":2891},[607,7775,5332],{"class":2895},[607,7777,2915],{"class":2914},[607,7779,7780,7782,7784,7786,7788],{"class":2887,"line":2918},[607,7781,5301],{"class":2891},[607,7783,1150],{"class":2895},[607,7785,3066],{"class":2891},[607,7787,6742],{"class":2895},[607,7789,6745],{"class":2914},[607,7791,7792,7794,7796,7798,7800],{"class":2887,"line":2942},[607,7793,6750],{"class":2891},[607,7795,1150],{"class":2895},[607,7797,4788],{"class":2891},[607,7799,6757],{"class":2895},[607,7801,6760],{"class":2914},[6807,7803],{},[6799,7805,7807,7808,4328],{"id":7806},"combien-de-bits-pour-nnn","Combien de bits pour ",[607,7809,7811,7824],{"className":7810},[610],[607,7812,7814],{"className":7813},[614],[616,7815,7816],{"xmlns":618},[620,7817,7818,7822],{},[623,7819,7820],{},[875,7821,1611],{},[636,7823,1611],{"encoding":638},[607,7825,7827],{"className":7826,"ariaHidden":644},[643],[607,7828,7830,7833],{"className":7829},[648],[607,7831],{"className":7832,"style":1664},[652],[607,7834,1611],{"className":7835,"style":1668},[657,893],[598,7837,4347,7838,7866,7867,1042,7895,2096],{},[607,7839,7841,7854],{"className":7840},[610],[607,7842,7844],{"className":7843},[614],[616,7845,7846],{"xmlns":618},[620,7847,7848,7852],{},[623,7849,7850],{},[875,7851,1161],{},[636,7853,1161],{"encoding":638},[607,7855,7857],{"className":7856,"ariaHidden":644},[643],[607,7858,7860,7863],{"className":7859},[648],[607,7861],{"className":7862,"style":4373},[652],[607,7864,1161],{"className":7865},[657,893]," bits, on couvre ",[607,7868,7870,7883],{"className":7869},[610],[607,7871,7873],{"className":7872},[614],[616,7874,7875],{"xmlns":618},[620,7876,7877,7881],{},[623,7878,7879],{},[629,7880,634],{},[636,7882,634],{"encoding":638},[607,7884,7886],{"className":7885,"ariaHidden":644},[643],[607,7887,7889,7892],{"className":7888},[648],[607,7890],{"className":7891,"style":980},[652],[607,7893,634],{"className":7894},[657],[607,7896,7898,7919],{"className":7897},[610],[607,7899,7901],{"className":7900},[614],[616,7902,7903],{"xmlns":618},[620,7904,7905,7917],{},[623,7906,7907,7913,7915],{},[626,7908,7909,7911],{},[629,7910,781],{},[875,7912,1161],{},[941,7914,1059],{},[629,7916,658],{},[636,7918,4491],{"encoding":638},[607,7920,7922,7966],{"className":7921,"ariaHidden":644},[643],[607,7923,7925,7928,7957,7960,7963],{"className":7924},[648],[607,7926],{"className":7927,"style":4501},[652],[607,7929,7931,7934],{"className":7930},[657],[607,7932,781],{"className":7933},[657],[607,7935,7937],{"className":7936},[668],[607,7938,7940],{"className":7939},[672],[607,7941,7943],{"className":7942},[676],[607,7944,7946],{"className":7945,"style":4408},[680],[607,7947,7948,7951],{"style":683},[607,7949],{"className":7950,"style":688},[687],[607,7952,7954],{"className":7953},[692,693,694,695],[607,7955,1161],{"className":7956},[657,893,695],[607,7958],{"className":7959,"style":1081},[965],[607,7961,1059],{"className":7962},[1085],[607,7964],{"className":7965,"style":1081},[965],[607,7967,7969,7972],{"className":7968},[648],[607,7970],{"className":7971,"style":980},[652],[607,7973,658],{"className":7974},[657],[1858,7976,7977,7985],{},[1861,7978,7979],{},[1864,7980,7981,7983],{},[1867,7982,4557],{},[1867,7984,4563],{},[1880,7986,7987,7993,8000],{},[1864,7988,7989,7991],{},[1885,7990,1907],{},[1885,7992,4788],{},[1864,7994,7995,7997],{},[1885,7996,1944],{},[1885,7998,7999],{},"65 535",[1864,8001,8002,8004],{},[1885,8003,4952],{},[1885,8005,8006],{},"≈ 4 milliards",[6807,8008],{},[6799,8010,8012],{"id":8011},"à-retenir","À retenir",[598,8014,8015,8018,2065,8046,2065,8125,8208],{},[602,8016,8017],{},"Un nombre n'a pas de base intrinsèque : seule son écriture en a une.",[607,8019,8021,8034],{"className":8020},[610],[607,8022,8024],{"className":8023},[614],[616,8025,8026],{"xmlns":618},[620,8027,8028,8032],{},[623,8029,8030],{},[629,8031,2050],{},[636,8033,2050],{"encoding":638},[607,8035,8037],{"className":8036,"ariaHidden":644},[643],[607,8038,8040,8043],{"className":8039},[648],[607,8041],{"className":8042,"style":980},[652],[607,8044,2050],{"className":8045},[657],[607,8047,8049,8070],{"className":8048},[610],[607,8050,8052],{"className":8051},[614],[616,8053,8054],{"xmlns":618},[620,8055,8056,8068],{},[623,8057,8058,8060,8062],{},[941,8059,1150],{"stretchy":1149},[629,8061,2119],{},[1152,8063,8064,8066],{},[941,8065,1197],{"stretchy":1149},[629,8067,781],{},[636,8069,2128],{"encoding":638},[607,8071,8073],{"className":8072,"ariaHidden":644},[643],[607,8074,8076,8079,8082,8085],{"className":8075},[648],[607,8077],{"className":8078,"style":1212},[652],[607,8080,1150],{"className":8081},[1216],[607,8083,2119],{"className":8084},[657],[607,8086,8088,8091],{"className":8087},[1416],[607,8089,1197],{"className":8090},[1416],[607,8092,8094],{"className":8093},[668],[607,8095,8097,8117],{"className":8096},[672,1229],[607,8098,8100,8114],{"className":8099},[676],[607,8101,8103],{"className":8102,"style":1236},[680],[607,8104,8105,8108],{"style":1239},[607,8106],{"className":8107,"style":688},[687],[607,8109,8111],{"className":8110},[692,693,694,695],[607,8112,781],{"className":8113},[657,695],[607,8115,1262],{"className":8116},[1261],[607,8118,8120],{"className":8119},[676],[607,8121,8123],{"className":8122,"style":1370},[680],[607,8124],{},[607,8126,8128,8150],{"className":8127},[610],[607,8129,8131],{"className":8130},[614],[616,8132,8133],{"xmlns":618},[620,8134,8135,8147],{},[623,8136,8137,8139,8141],{},[941,8138,1150],{"stretchy":1149},[875,8140,2034],{},[1152,8142,8143,8145],{},[941,8144,1197],{"stretchy":1149},[629,8146,1944],{},[636,8148,8149],{"encoding":638},"(B)_{16}",[607,8151,8153],{"className":8152,"ariaHidden":644},[643],[607,8154,8156,8159,8162,8165],{"className":8155},[648],[607,8157],{"className":8158,"style":1212},[652],[607,8160,1150],{"className":8161},[1216],[607,8163,2034],{"className":8164,"style":2230},[657,893],[607,8166,8168,8171],{"className":8167},[1416],[607,8169,1197],{"className":8170},[1416],[607,8172,8174],{"className":8173},[668],[607,8175,8177,8200],{"className":8176},[672,1229],[607,8178,8180,8197],{"className":8179},[676],[607,8181,8183],{"className":8182,"style":1236},[680],[607,8184,8185,8188],{"style":1239},[607,8186],{"className":8187,"style":688},[687],[607,8189,8191],{"className":8190},[692,693,694,695],[607,8192,8194],{"className":8193},[657,695],[607,8195,1944],{"className":8196},[657,695],[607,8198,1262],{"className":8199},[1261],[607,8201,8203],{"className":8202},[676],[607,8204,8206],{"className":8205,"style":1370},[680],[607,8207],{}," désignent la même quantité.",[5620,8210,6778],{},{"title":2882,"searchDepth":2918,"depth":2918,"links":8212},[],"Deck pour la séance sur le binaire, l'hexadécimal et les 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