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tables","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Ftraitement-tables","0.snt-2nde\u002Fsd-donnees-structurees\u002F4.traitement-tables",{"title":115,"path":116,"stem":117},"Le cloud","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Fcloud","0.snt-2nde\u002Fsd-donnees-structurees\u002F5.cloud",{"title":119,"path":120,"stem":121,"children":122},"Localisation, cartographie et mobilité","\u002Fsnt-2nde\u002Fse-localisation-cartographie","0.snt-2nde\u002Fse-localisation-cartographie\u002F0.index",[123,124,128,132,136,140],{"title":119,"path":120,"stem":121},{"title":125,"path":126,"stem":127},"GPS et Galileo — se situer grâce aux satellites","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fgps-galileo","0.snt-2nde\u002Fse-localisation-cartographie\u002F1.gps-galileo",{"title":129,"path":130,"stem":131},"Décoder une trame NMEA","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Ftrame-nmea","0.snt-2nde\u002Fse-localisation-cartographie\u002F2.trame-nmea",{"title":133,"path":134,"stem":135},"Cartes numériques — GeoPortail et OpenStreetMap","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fcartes-numeriques","0.snt-2nde\u002Fse-localisation-cartographie\u002F3.cartes-numeriques",{"title":137,"path":138,"stem":139},"Itinéraires et graphes","\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Fitineraires-graphes","0.snt-2nde\u002Fse-localisation-cartographie\u002F4.itineraires-graphes",{"title":141,"path":142,"stem":143},"Confidentialité de la 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 connectés","\u002Fsnt-2nde\u002Fsf-info-embarquee\u002Fihm-objet-connecte","0.snt-2nde\u002Fsf-info-embarquee\u002F3.ihm-objet-connecte",{"title":163,"path":164,"stem":165,"children":166},"Photographie numérique","\u002Fsnt-2nde\u002Fsg-photo-numerique","0.snt-2nde\u002Fsg-photo-numerique\u002F0.index",[167,168,172,176,180],{"title":163,"path":164,"stem":165},{"title":169,"path":170,"stem":171},"Photosites, pixels et résolution","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Fpixels-resolution","0.snt-2nde\u002Fsg-photo-numerique\u002F1.pixels-resolution",{"title":173,"path":174,"stem":175},"Les algorithmes de l'appareil photo","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Falgorithmes-photo","0.snt-2nde\u002Fsg-photo-numerique\u002F2.algorithmes-photo",{"title":177,"path":178,"stem":179},"Les métadonnées EXIF","\u002Fsnt-2nde\u002Fsg-photo-numerique\u002Fmetadonnees-exif","0.snt-2nde\u002Fsg-photo-numerique\u002F3.metadonnees-exif",{"title":181,"path":182,"stem":183},"Traiter une image en 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 — Première","\u002Fnsi-1ere","1.nsi-1ere\u002F0.index",[229,230,234,256,282,304,328,354,380,410],{"title":225,"path":226,"stem":227},{"title":231,"path":232,"stem":233},"Relecture pédagogique — 8 chapitres NSI 1ère (PA → PH)","\u002Fnsi-1ere\u002Freview","1.nsi-1ere\u002FREVIEW",{"title":235,"path":236,"stem":237,"children":238},"Histoire de l'informatique","\u002Fnsi-1ere\u002Fpa-histoire-info","1.nsi-1ere\u002Fpa-histoire-info\u002F0.index",[239,240,244,248,252],{"title":235,"path":236,"stem":237},{"title":241,"path":242,"stem":243},"De la préantiquité aux machines à calculer","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Fpreantiquite-aux-machines","1.nsi-1ere\u002Fpa-histoire-info\u002F1.preantiquite-aux-machines",{"title":245,"path":246,"stem":247},"La machine universelle (1930-1950)","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Fmachine-universelle","1.nsi-1ere\u002Fpa-histoire-info\u002F2.machine-universelle",{"title":249,"path":250,"stem":251},"Les ordinateurs modernes (1947-1990)","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Fordinateurs-modernes","1.nsi-1ere\u002Fpa-histoire-info\u002F3.ordinateurs-modernes",{"title":253,"path":254,"stem":255},"Réseaux, Web et IA (1969 à aujourd'hui)","\u002Fnsi-1ere\u002Fpa-histoire-info\u002Freseaux-et-web","1.nsi-1ere\u002Fpa-histoire-info\u002F4.reseaux-et-web",{"title":257,"path":258,"stem":259,"children":260},"Représentation des données — types et valeurs","\u002Fnsi-1ere\u002Fpb-types-valeurs","1.nsi-1ere\u002Fpb-types-valeurs\u002F0.index",[261,262,266,270,274,278],{"title":257,"path":258,"stem":259},{"title":263,"path":264,"stem":265},"Bases de numération et entiers positifs","\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fbases-entiers-positifs","1.nsi-1ere\u002Fpb-types-valeurs\u002F1.bases-entiers-positifs",{"title":267,"path":268,"stem":269},"Entiers relatifs et complément à 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 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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":279,"bo":587,"body":589,"description":2543,"eval":2544,"extension":2545,"labo":2544,"meta":2546,"navigation":2547,"path":280,"quizzes":2548,"readingTime":853,"seo":2559,"stem":281,"tp":2544,"__hash__":2560},"cours\u002F1.nsi-1ere\u002Fpb-types-valeurs\u002F5.booleens.md",[588],"PB05",{"type":590,"value":591,"toc":2524},"minimark",[592,597,618,632,644,648,651,838,942,945,953,957,964,971,1136,1142,1301,1307,1393,1504,1511,1557,1715,1725,1761,1826,1850,1854,1869,1887,1894,1918,1965,1985,2012,2016,2033,2060,2067,2127,2141,2151,2155,2162,2182,2398,2408,2412,2498,2502,2520],[593,594,596],"h2",{"id":595},"introduction","Introduction",[598,599,600,601,605,606,609,610,613,614,617],"p",{},"Tout programme prend, à un moment ou un autre, des ",[602,603,604],"strong",{},"décisions"," : « si ce\nnombre est positif, faire ceci, sinon cela ». Ces décisions s'appuient sur des\n",[602,607,608],{},"conditions",", qui ne peuvent avoir que deux résultats : ",[602,611,612],{},"vrai"," ou ",[602,615,616],{},"faux",".",[598,619,620,621,624,625,628,629],{},"Cette logique binaire, formalisée au XIXᵉ siècle par le mathématicien anglais\nGeorge Boole, porte aujourd'hui son nom : on parle d'",[602,622,623],{},"algèbre de Boole"," et\nde ",[602,626,627],{},"valeurs booléennes",". Elle est partout en informatique — des tests\nd'égalité jusqu'aux portes logiques qui constituent physiquement le\nprocesseur. ",[630,631],"bo-ref",{"code":588},[598,633,634,635,639,640,643],{},"En Python, ces deux valeurs s'écrivent ",[636,637,638],"code",{},"True"," et ",[636,641,642],{},"False"," (avec une majuscule\ninitiale, c'est important).",[593,645,647],{"id":646},"les-trois-opérateurs-de-base","Les trois opérateurs de base",[598,649,650],{},"L'algèbre de Boole repose sur trois opérateurs principaux. En Python, ils\ns'écrivent en toutes lettres.",[652,653,654,673],"table",{},[655,656,657],"thead",{},[658,659,660,664,667,670],"tr",{},[661,662,663],"th",{},"Opérateur logique",[661,665,666],{},"Python",[661,668,669],{},"Notation mathématique",[661,671,672],{},"Effet",[674,675,676,742,790],"tbody",{},[658,677,678,682,687,735],{},[679,680,681],"td",{},"ET",[679,683,684],{},[636,685,686],{},"and",[679,688,689],{},[690,691,694,717],"span",{"className":692},[693],"katex",[690,695,698],{"className":696},[697],"katex-mathml",[699,700,702],"math",{"xmlns":701},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[703,704,705,712],"semantics",{},[706,707,708],"mrow",{},[709,710,711],"mo",{},"∧",[713,714,716],"annotation",{"encoding":715},"application\u002Fx-tex","\\land",[690,718,722],{"className":719,"ariaHidden":721},[720],"katex-html","true",[690,723,726,731],{"className":724},[725],"base",[690,727],{"className":728,"style":730},[729],"strut","height:0.5556em;",[690,732,711],{"className":733},[734],"mord",[679,736,737,738,741],{},"vrai si ",[602,739,740],{},"les deux"," opérandes sont vrais",[658,743,744,747,752,784],{},[679,745,746],{},"OU",[679,748,749],{},[636,750,751],{},"or",[679,753,754],{},[690,755,757,772],{"className":756},[693],[690,758,760],{"className":759},[697],[699,761,762],{"xmlns":701},[703,763,764,769],{},[706,765,766],{},[709,767,768],{},"∨",[713,770,771],{"encoding":715},"\\lor",[690,773,775],{"className":774,"ariaHidden":721},[720],[690,776,778,781],{"className":777},[725],[690,779],{"className":780,"style":730},[729],[690,782,768],{"className":783},[734],[679,785,737,786,789],{},[602,787,788],{},"au moins un"," des opérandes est vrai",[658,791,792,795,800,835],{},[679,793,794],{},"NON",[679,796,797],{},[636,798,799],{},"not",[679,801,802],{},[690,803,805,822],{"className":804},[693],[690,806,808],{"className":807},[697],[699,809,810],{"xmlns":701},[703,811,812,819],{},[706,813,814],{},[815,816,818],"mi",{"mathvariant":817},"normal","¬",[713,820,821],{"encoding":715},"\\lnot",[690,823,825],{"className":824,"ariaHidden":721},[720],[690,826,828,832],{"className":827},[725],[690,829],{"className":830,"style":831},[729],"height:0.4306em;",[690,833,818],{"className":834},[734],[679,836,837],{},"inverse la valeur",[839,840,841],"python-snippet",{},[842,843,848],"pre",{"className":844,"code":845,"language":846,"meta":847,"style":847},"language-python shiki shiki-themes github-light github-light github-dark","print(True and False)   # False\nprint(True or False)    # True\nprint(not True)         # False\nprint(not (5 > 3))      # False, car 5 > 3 est True\n","python","",[636,849,850,878,898,915],{"__ignoreMap":847},[690,851,854,858,862,864,868,871,874],{"class":852,"line":853},"line",1,[690,855,857],{"class":856},"sBjJW","print",[690,859,861],{"class":860},"sxrX7","(",[690,863,638],{"class":856},[690,865,867],{"class":866},"s8jYJ"," and",[690,869,870],{"class":856}," False",[690,872,873],{"class":860},")   ",[690,875,877],{"class":876},"sCsY4","# False\n",[690,879,881,883,885,887,890,892,895],{"class":852,"line":880},2,[690,882,857],{"class":856},[690,884,861],{"class":860},[690,886,638],{"class":856},[690,888,889],{"class":866}," or",[690,891,870],{"class":856},[690,893,894],{"class":860},")    ",[690,896,897],{"class":876},"# True\n",[690,899,901,903,905,907,910,913],{"class":852,"line":900},3,[690,902,857],{"class":856},[690,904,861],{"class":860},[690,906,799],{"class":866},[690,908,909],{"class":856}," True",[690,911,912],{"class":860},")         ",[690,914,877],{"class":876},[690,916,918,920,922,924,927,930,933,936,939],{"class":852,"line":917},4,[690,919,857],{"class":856},[690,921,861],{"class":860},[690,923,799],{"class":866},[690,925,926],{"class":860}," (",[690,928,929],{"class":856},"5",[690,931,932],{"class":866}," >",[690,934,935],{"class":856}," 3",[690,937,938],{"class":860},"))      ",[690,940,941],{"class":876},"# False, car 5 > 3 est True\n",[598,943,944],{},"Sortie attendue :",[842,946,951],{"className":947,"code":949,"language":950},[948],"language-text","False\nTrue\nFalse\nFalse\n","text",[636,952,949],{"__ignoreMap":847},[593,954,956],{"id":955},"tables-de-vérité","Tables de vérité",[598,958,959,960,963],{},"Une ",[602,961,962],{},"table de vérité"," énumère toutes les combinaisons possibles des\nopérandes et donne la valeur du résultat. C'est l'outil de référence pour\nanalyser une expression booléenne.",[965,966,968,970],"h3",{"id":967},"and-et-logique",[636,969,686],{}," (ET logique)",[652,972,973,1098],{},[655,974,975],{},[658,976,977,1010,1042],{},[661,978,979],{},[690,980,982,996],{"className":981},[693],[690,983,985],{"className":984},[697],[699,986,987],{"xmlns":701},[703,988,989,994],{},[706,990,991],{},[815,992,993],{},"A",[713,995,993],{"encoding":715},[690,997,999],{"className":998,"ariaHidden":721},[720],[690,1000,1002,1006],{"className":1001},[725],[690,1003],{"className":1004,"style":1005},[729],"height:0.6833em;",[690,1007,993],{"className":1008},[734,1009],"mathnormal",[661,1011,1012],{},[690,1013,1015,1029],{"className":1014},[693],[690,1016,1018],{"className":1017},[697],[699,1019,1020],{"xmlns":701},[703,1021,1022,1027],{},[706,1023,1024],{},[815,1025,1026],{},"B",[713,1028,1026],{"encoding":715},[690,1030,1032],{"className":1031,"ariaHidden":721},[720],[690,1033,1035,1038],{"className":1034},[725],[690,1036],{"className":1037,"style":1005},[729],[690,1039,1026],{"className":1040,"style":1041},[734,1009],"margin-right:0.0502em;",[661,1043,1044],{},[690,1045,1047,1065],{"className":1046},[693],[690,1048,1050],{"className":1049},[697],[699,1051,1052],{"xmlns":701},[703,1053,1054,1062],{},[706,1055,1056,1058,1060],{},[815,1057,993],{},[709,1059,711],{},[815,1061,1026],{},[713,1063,1064],{"encoding":715},"A \\land B",[690,1066,1068,1089],{"className":1067,"ariaHidden":721},[720],[690,1069,1071,1074,1077,1082,1086],{"className":1070},[725],[690,1072],{"className":1073,"style":1005},[729],[690,1075,993],{"className":1076},[734,1009],[690,1078],{"className":1079,"style":1081},[1080],"mspace","margin-right:0.2222em;",[690,1083,711],{"className":1084},[1085],"mbin",[690,1087],{"className":1088,"style":1081},[1080],[690,1090,1092,1095],{"className":1091},[725],[690,1093],{"className":1094,"style":1005},[729],[690,1096,1026],{"className":1097,"style":1041},[734,1009],[674,1099,1100,1109,1118,1126],{},[658,1101,1102,1105,1107],{},[679,1103,1104],{},"Faux",[679,1106,1104],{},[679,1108,1104],{},[658,1110,1111,1113,1116],{},[679,1112,1104],{},[679,1114,1115],{},"Vrai",[679,1117,1104],{},[658,1119,1120,1122,1124],{},[679,1121,1115],{},[679,1123,1104],{},[679,1125,1104],{},[658,1127,1128,1130,1132],{},[679,1129,1115],{},[679,1131,1115],{},[679,1133,1134],{},[602,1135,1115],{},[965,1137,1139,1141],{"id":1138},"or-ou-logique",[636,1140,751],{}," (OU logique)",[652,1143,1144,1261],{},[655,1145,1146],{},[658,1147,1148,1178,1208],{},[661,1149,1150],{},[690,1151,1153,1166],{"className":1152},[693],[690,1154,1156],{"className":1155},[697],[699,1157,1158],{"xmlns":701},[703,1159,1160,1164],{},[706,1161,1162],{},[815,1163,993],{},[713,1165,993],{"encoding":715},[690,1167,1169],{"className":1168,"ariaHidden":721},[720],[690,1170,1172,1175],{"className":1171},[725],[690,1173],{"className":1174,"style":1005},[729],[690,1176,993],{"className":1177},[734,1009],[661,1179,1180],{},[690,1181,1183,1196],{"className":1182},[693],[690,1184,1186],{"className":1185},[697],[699,1187,1188],{"xmlns":701},[703,1189,1190,1194],{},[706,1191,1192],{},[815,1193,1026],{},[713,1195,1026],{"encoding":715},[690,1197,1199],{"className":1198,"ariaHidden":721},[720],[690,1200,1202,1205],{"className":1201},[725],[690,1203],{"className":1204,"style":1005},[729],[690,1206,1026],{"className":1207,"style":1041},[734,1009],[661,1209,1210],{},[690,1211,1213,1231],{"className":1212},[693],[690,1214,1216],{"className":1215},[697],[699,1217,1218],{"xmlns":701},[703,1219,1220,1228],{},[706,1221,1222,1224,1226],{},[815,1223,993],{},[709,1225,768],{},[815,1227,1026],{},[713,1229,1230],{"encoding":715},"A \\lor B",[690,1232,1234,1252],{"className":1233,"ariaHidden":721},[720],[690,1235,1237,1240,1243,1246,1249],{"className":1236},[725],[690,1238],{"className":1239,"style":1005},[729],[690,1241,993],{"className":1242},[734,1009],[690,1244],{"className":1245,"style":1081},[1080],[690,1247,768],{"className":1248},[1085],[690,1250],{"className":1251,"style":1081},[1080],[690,1253,1255,1258],{"className":1254},[725],[690,1256],{"className":1257,"style":1005},[729],[690,1259,1026],{"className":1260,"style":1041},[734,1009],[674,1262,1263,1271,1281,1291],{},[658,1264,1265,1267,1269],{},[679,1266,1104],{},[679,1268,1104],{},[679,1270,1104],{},[658,1272,1273,1275,1277],{},[679,1274,1104],{},[679,1276,1115],{},[679,1278,1279],{},[602,1280,1115],{},[658,1282,1283,1285,1287],{},[679,1284,1115],{},[679,1286,1104],{},[679,1288,1289],{},[602,1290,1115],{},[658,1292,1293,1295,1297],{},[679,1294,1115],{},[679,1296,1115],{},[679,1298,1299],{},[602,1300,1115],{},[965,1302,1304,1306],{"id":1303},"not-non-logique",[636,1305,799],{}," (NON logique)",[652,1308,1309,1379],{},[655,1310,1311],{},[658,1312,1313,1343],{},[661,1314,1315],{},[690,1316,1318,1331],{"className":1317},[693],[690,1319,1321],{"className":1320},[697],[699,1322,1323],{"xmlns":701},[703,1324,1325,1329],{},[706,1326,1327],{},[815,1328,993],{},[713,1330,993],{"encoding":715},[690,1332,1334],{"className":1333,"ariaHidden":721},[720],[690,1335,1337,1340],{"className":1336},[725],[690,1338],{"className":1339,"style":1005},[729],[690,1341,993],{"className":1342},[734,1009],[661,1344,1345],{},[690,1346,1348,1364],{"className":1347},[693],[690,1349,1351],{"className":1350},[697],[699,1352,1353],{"xmlns":701},[703,1354,1355,1361],{},[706,1356,1357,1359],{},[815,1358,818],{"mathvariant":817},[815,1360,993],{},[713,1362,1363],{"encoding":715},"\\lnot A",[690,1365,1367],{"className":1366,"ariaHidden":721},[720],[690,1368,1370,1373,1376],{"className":1369},[725],[690,1371],{"className":1372,"style":1005},[729],[690,1374,818],{"className":1375},[734],[690,1377,993],{"className":1378},[734,1009],[674,1380,1381,1387],{},[658,1382,1383,1385],{},[679,1384,1104],{},[679,1386,1115],{},[658,1388,1389,1391],{},[679,1390,1115],{},[679,1392,1104],{},[1394,1395,1396],"note",{},[598,1397,1398,1399,1428,1429,1503],{},"Pour ",[690,1400,1402,1416],{"className":1401},[693],[690,1403,1405],{"className":1404},[697],[699,1406,1407],{"xmlns":701},[703,1408,1409,1414],{},[706,1410,1411],{},[815,1412,1413],{},"n",[713,1415,1413],{"encoding":715},[690,1417,1419],{"className":1418,"ariaHidden":721},[720],[690,1420,1422,1425],{"className":1421},[725],[690,1423],{"className":1424,"style":831},[729],[690,1426,1413],{"className":1427},[734,1009]," variables booléennes, la table de vérité contient ",[690,1430,1432,1453],{"className":1431},[693],[690,1433,1435],{"className":1434},[697],[699,1436,1437],{"xmlns":701},[703,1438,1439,1450],{},[706,1440,1441],{},[1442,1443,1444,1448],"msup",{},[1445,1446,1447],"mn",{},"2",[815,1449,1413],{},[713,1451,1452],{"encoding":715},"2^n",[690,1454,1456],{"className":1455,"ariaHidden":721},[720],[690,1457,1459,1463],{"className":1458},[725],[690,1460],{"className":1461,"style":1462},[729],"height:0.6644em;",[690,1464,1466,1469],{"className":1465},[734],[690,1467,1447],{"className":1468},[734],[690,1470,1473],{"className":1471},[1472],"msupsub",[690,1474,1477],{"className":1475},[1476],"vlist-t",[690,1478,1481],{"className":1479},[1480],"vlist-r",[690,1482,1485],{"className":1483,"style":1462},[1484],"vlist",[690,1486,1488,1493],{"style":1487},"top:-3.063em;margin-right:0.05em;",[690,1489],{"className":1490,"style":1492},[1491],"pstrut","height:2.7em;",[690,1494,1500],{"className":1495},[1496,1497,1498,1499],"sizing","reset-size6","size3","mtight",[690,1501,1413],{"className":1502},[734,1009,1499]," lignes —\ntoutes les combinaisons possibles. Pour 3 variables, 8 lignes ; pour 4\nvariables, 16. La taille double à chaque ajout.",[593,1505,1507,1508],{"id":1506},"le-ou-exclusif-xor","Le ou exclusif — ",[636,1509,1510],{},"xor",[598,1512,1513,1514,1517,1518,1520,1521,1552,1553,1556],{},"Il existe un quatrième opérateur très utile : le ",[602,1515,1516],{},"ou exclusif",", noté ",[636,1519,1510],{},"\nou ",[690,1522,1524,1539],{"className":1523},[693],[690,1525,1527],{"className":1526},[697],[699,1528,1529],{"xmlns":701},[703,1530,1531,1536],{},[706,1532,1533],{},[709,1534,1535],{},"⊕",[713,1537,1538],{"encoding":715},"\\oplus",[690,1540,1542],{"className":1541,"ariaHidden":721},[720],[690,1543,1545,1549],{"className":1544},[725],[690,1546],{"className":1547,"style":1548},[729],"height:0.6667em;vertical-align:-0.0833em;",[690,1550,1535],{"className":1551},[734],". Il vaut ",[602,1554,1555],{},"vrai si exactement un"," des opérandes est vrai (et donc\nfaux si les deux sont identiques).",[652,1558,1559,1677],{},[655,1560,1561],{},[658,1562,1563,1593,1623],{},[661,1564,1565],{},[690,1566,1568,1581],{"className":1567},[693],[690,1569,1571],{"className":1570},[697],[699,1572,1573],{"xmlns":701},[703,1574,1575,1579],{},[706,1576,1577],{},[815,1578,993],{},[713,1580,993],{"encoding":715},[690,1582,1584],{"className":1583,"ariaHidden":721},[720],[690,1585,1587,1590],{"className":1586},[725],[690,1588],{"className":1589,"style":1005},[729],[690,1591,993],{"className":1592},[734,1009],[661,1594,1595],{},[690,1596,1598,1611],{"className":1597},[693],[690,1599,1601],{"className":1600},[697],[699,1602,1603],{"xmlns":701},[703,1604,1605,1609],{},[706,1606,1607],{},[815,1608,1026],{},[713,1610,1026],{"encoding":715},[690,1612,1614],{"className":1613,"ariaHidden":721},[720],[690,1615,1617,1620],{"className":1616},[725],[690,1618],{"className":1619,"style":1005},[729],[690,1621,1026],{"className":1622,"style":1041},[734,1009],[661,1624,1625],{},[690,1626,1628,1646],{"className":1627},[693],[690,1629,1631],{"className":1630},[697],[699,1632,1633],{"xmlns":701},[703,1634,1635,1643],{},[706,1636,1637,1639,1641],{},[815,1638,993],{},[709,1640,1535],{},[815,1642,1026],{},[713,1644,1645],{"encoding":715},"A \\oplus B",[690,1647,1649,1668],{"className":1648,"ariaHidden":721},[720],[690,1650,1652,1656,1659,1662,1665],{"className":1651},[725],[690,1653],{"className":1654,"style":1655},[729],"height:0.7667em;vertical-align:-0.0833em;",[690,1657,993],{"className":1658},[734,1009],[690,1660],{"className":1661,"style":1081},[1080],[690,1663,1535],{"className":1664},[1085],[690,1666],{"className":1667,"style":1081},[1080],[690,1669,1671,1674],{"className":1670},[725],[690,1672],{"className":1673,"style":1005},[729],[690,1675,1026],{"className":1676,"style":1041},[734,1009],[674,1678,1679,1687,1697,1707],{},[658,1680,1681,1683,1685],{},[679,1682,1104],{},[679,1684,1104],{},[679,1686,1104],{},[658,1688,1689,1691,1693],{},[679,1690,1104],{},[679,1692,1115],{},[679,1694,1695],{},[602,1696,1115],{},[658,1698,1699,1701,1703],{},[679,1700,1115],{},[679,1702,1104],{},[679,1704,1705],{},[602,1706,1115],{},[658,1708,1709,1711,1713],{},[679,1710,1115],{},[679,1712,1115],{},[679,1714,1104],{},[598,1716,1717,1718,1720,1721,1724],{},"Python ne fournit pas d'opérateur ",[636,1719,1510],{}," en toutes lettres pour les booléens,\nmais on peut l'écrire avec ",[636,1722,1723],{},"!="," :",[842,1726,1728],{"className":844,"code":1727,"language":846,"meta":847,"style":847},"A, B = True, False\nprint(A != B)   # True — équivaut à A xor B\n",[636,1729,1730,1746],{"__ignoreMap":847},[690,1731,1732,1735,1738,1740,1743],{"class":852,"line":853},[690,1733,1734],{"class":860},"A, B ",[690,1736,1737],{"class":866},"=",[690,1739,909],{"class":856},[690,1741,1742],{"class":860},", ",[690,1744,1745],{"class":856},"False\n",[690,1747,1748,1750,1753,1755,1758],{"class":852,"line":880},[690,1749,857],{"class":856},[690,1751,1752],{"class":860},"(A ",[690,1754,1723],{"class":866},[690,1756,1757],{"class":860}," B)   ",[690,1759,1760],{"class":876},"# True — équivaut à A xor B\n",[598,1762,1763,1764,1766,1767,1770,1771,1825],{},"Le ",[636,1765,1510],{}," est très utile pour l'",[602,1768,1769],{},"addition binaire"," : sur 1 bit, ",[690,1772,1774,1793],{"className":1773},[693],[690,1775,1777],{"className":1776},[697],[699,1778,1779],{"xmlns":701},[703,1780,1781,1790],{},[706,1782,1783,1786,1788],{},[1445,1784,1785],{},"1",[709,1787,1535],{},[1445,1789,1785],{},[713,1791,1792],{"encoding":715},"1 \\oplus 1",[690,1794,1796,1815],{"className":1795,"ariaHidden":721},[720],[690,1797,1799,1803,1806,1809,1812],{"className":1798},[725],[690,1800],{"className":1801,"style":1802},[729],"height:0.7278em;vertical-align:-0.0833em;",[690,1804,1785],{"className":1805},[734],[690,1807],{"className":1808,"style":1081},[1080],[690,1810,1535],{"className":1811},[1085],[690,1813],{"className":1814,"style":1081},[1080],[690,1816,1818,1822],{"className":1817},[725],[690,1819],{"className":1820,"style":1821},[729],"height:0.6444em;",[690,1823,1785],{"className":1824},[734],"\nvaut 0 avec une retenue. C'est exactement ce dont a besoin un additionneur\nmatériel.",[1827,1828,1830,1836],"self-eval-qcm",{"correct":1447,"slug":1829},"booleens-c1",[1831,1832,1833],"template",{"v-slot:question":847},[598,1834,1835],{},"Quel opérateur retourne vrai uniquement si A et B sont différents ?",[1831,1837,1838],{"v-slot:choices":847},[1839,1840,1841,1844,1846,1848],"ul",{},[1842,1843,686],"li",{},[1842,1845,751],{},[1842,1847,1510],{},[1842,1849,799],{},[593,1851,1853],{"id":1852},"expressions-booléennes","Expressions booléennes",[598,1855,1856,1857,1742,1859,1861,1862,1864,1865,1868],{},"On peut composer des expressions plus complexes en combinant ",[636,1858,686],{},[636,1860,751],{},",\n",[636,1863,799],{},". Comme en arithmétique, ",[602,1866,1867],{},"l'ordre des opérations"," compte :",[1870,1871,1872,1877,1882],"ol",{},[1842,1873,1874,1876],{},[636,1875,799],{}," est appliqué en premier (priorité la plus haute).",[1842,1878,1879,1880,617],{},"Puis ",[636,1881,686],{},[1842,1883,1879,1884,1886],{},[636,1885,751],{}," (priorité la plus basse).",[598,1888,1889,1890,1893],{},"Exemple : pour évaluer ",[636,1891,1892],{},"True or False and not False",", on lit dans cet ordre :",[1870,1895,1896,1904,1911],{},[1842,1897,1898,1901,1902],{},[636,1899,1900],{},"not False"," → ",[636,1903,638],{},[1842,1905,1906,1901,1909],{},[636,1907,1908],{},"False and True",[636,1910,642],{},[1842,1912,1913,1901,1916],{},[636,1914,1915],{},"True or False",[636,1917,638],{},[1919,1920,1921,1928],"tip",{},[598,1922,1923,1924,1927],{},"En cas de doute, ",[602,1925,1926],{},"mettez des parenthèses",". Elles ne coûtent rien et\nclarifient la lecture du code :",[842,1929,1931],{"className":844,"code":1930,"language":846,"meta":847,"style":847},"if (age >= 18) and (permis or accompagnateur):\n    conduire()\n",[636,1932,1933,1960],{"__ignoreMap":847},[690,1934,1935,1938,1941,1944,1947,1950,1952,1955,1957],{"class":852,"line":853},[690,1936,1937],{"class":866},"if",[690,1939,1940],{"class":860}," (age ",[690,1942,1943],{"class":866},">=",[690,1945,1946],{"class":856}," 18",[690,1948,1949],{"class":860},") ",[690,1951,686],{"class":866},[690,1953,1954],{"class":860}," (permis ",[690,1956,751],{"class":866},[690,1958,1959],{"class":860}," accompagnateur):\n",[690,1961,1962],{"class":852,"line":880},[690,1963,1964],{"class":860},"    conduire()\n",[1827,1966,1968,1977],{"correct":1785,"slug":1967},"booleens-c2",[1831,1969,1970],{"v-slot:question":847},[598,1971,1972,1973,1976],{},"Que vaut ",[636,1974,1975],{},"not (True or False)"," ?",[1831,1978,1979],{"v-slot:choices":847},[1839,1980,1981,1983],{},[1842,1982,638],{},[1842,1984,642],{},[1827,1986,1989,2004],{"correct":1987,"slug":1988},"0","booleens-c3",[1831,1990,1991],{"v-slot:question":847},[598,1992,1993,1994,1997,1998,2000,2001,2003],{},"Sans parenthèses, que vaut ",[636,1995,1996],{},"True or False and False"," (rappel : ",[636,1999,686],{}," est prioritaire sur ",[636,2002,751],{},") ?",[1831,2005,2006],{"v-slot:choices":847},[1839,2007,2008,2010],{},[1842,2009,638],{},[1842,2011,642],{},[593,2013,2015],{"id":2014},"le-caractère-séquentiel-des-opérateurs","Le caractère séquentiel des opérateurs",[598,2017,2018,2019,2022,2023,2026,2027,613,2030,617],{},"Une particularité importante : Python évalue les opérateurs booléens ",[602,2020,2021],{},"de\ngauche à droite",", et il ",[602,2024,2025],{},"s'arrête dès qu'il connaît le résultat",". On parle\nd'",[602,2028,2029],{},"évaluation paresseuse",[602,2031,2032],{},"séquentielle",[1839,2034,2035,2050],{},[1842,2036,1398,2037,2040,2041,2043,2044,2047,2048,617],{},[636,2038,2039],{},"A and B"," : si ",[636,2042,993],{}," est faux, le résultat est forcément faux. Python ne\nva même ",[602,2045,2046],{},"pas évaluer"," ",[636,2049,1026],{},[1842,2051,1398,2052,2040,2055,2057,2058,617],{},[636,2053,2054],{},"A or B",[636,2056,993],{}," est vrai, le résultat est forcément vrai. Python ne\nva même pas évaluer ",[636,2059,1026],{},[598,2061,2062,2063,2066],{},"Cette propriété est exploitée comme une ",[602,2064,2065],{},"protection"," courante :",[842,2068,2070],{"className":844,"code":2069,"language":846,"meta":847,"style":847},"liste = []\n# Sans court-circuit, on aurait une erreur en accédant à liste[0]\nif liste and liste[0] > 5:\n    print(\"Premier élément grand\")\n",[636,2071,2072,2082,2087,2113],{"__ignoreMap":847},[690,2073,2074,2077,2079],{"class":852,"line":853},[690,2075,2076],{"class":860},"liste ",[690,2078,1737],{"class":866},[690,2080,2081],{"class":860}," []\n",[690,2083,2084],{"class":852,"line":880},[690,2085,2086],{"class":876},"# Sans court-circuit, on aurait une erreur en accédant à liste[0]\n",[690,2088,2089,2091,2094,2096,2099,2101,2104,2107,2110],{"class":852,"line":900},[690,2090,1937],{"class":866},[690,2092,2093],{"class":860}," liste ",[690,2095,686],{"class":866},[690,2097,2098],{"class":860}," liste[",[690,2100,1987],{"class":856},[690,2102,2103],{"class":860},"] ",[690,2105,2106],{"class":866},">",[690,2108,2109],{"class":856}," 5",[690,2111,2112],{"class":860},":\n",[690,2114,2115,2118,2120,2124],{"class":852,"line":917},[690,2116,2117],{"class":856},"    print",[690,2119,861],{"class":860},[690,2121,2123],{"class":2122},"sIIMD","\"Premier élément grand\"",[690,2125,2126],{"class":860},")\n",[598,2128,2129,2130,2133,2134,2136,2137,2140],{},"Si ",[636,2131,2132],{},"liste"," est vide, ",[636,2135,2132],{}," est considéré comme faux, et Python ne tente même\npas d'évaluer ",[636,2138,2139],{},"liste[0]"," qui aurait planté.",[2142,2143,2144],"warning",{},[598,2145,2146,2147,2150],{},"Cette évaluation séquentielle peut surprendre quand un opérande contient un\n",[602,2148,2149],{},"effet de bord"," (appel de fonction, modification d'une variable). L'effet ne\nse produira pas si l'opérande n'est pas évalué. Toujours en avoir conscience.",[593,2152,2154],{"id":2153},"une-application-directe-laddition-binaire","Une application directe — l'addition binaire",[598,2156,2157,2158,639,2160,1724],{},"L'addition de deux bits se décompose élégamment avec ",[636,2159,1510],{},[636,2161,686],{},[1839,2163,2164,2173],{},[1842,2165,1763,2166,2169,2170,617],{},[602,2167,2168],{},"bit de résultat"," est donné par ",[636,2171,2172],{},"A xor B",[1842,2174,2175,2176,2179,2180,617],{},"La ",[602,2177,2178],{},"retenue"," est donnée par ",[636,2181,2039],{},[652,2183,2184,2354],{},[655,2185,2186],{},[658,2187,2188,2218,2248,2301],{},[661,2189,2190],{},[690,2191,2193,2206],{"className":2192},[693],[690,2194,2196],{"className":2195},[697],[699,2197,2198],{"xmlns":701},[703,2199,2200,2204],{},[706,2201,2202],{},[815,2203,993],{},[713,2205,993],{"encoding":715},[690,2207,2209],{"className":2208,"ariaHidden":721},[720],[690,2210,2212,2215],{"className":2211},[725],[690,2213],{"className":2214,"style":1005},[729],[690,2216,993],{"className":2217},[734,1009],[661,2219,2220],{},[690,2221,2223,2236],{"className":2222},[693],[690,2224,2226],{"className":2225},[697],[699,2227,2228],{"xmlns":701},[703,2229,2230,2234],{},[706,2231,2232],{},[815,2233,1026],{},[713,2235,1026],{"encoding":715},[690,2237,2239],{"className":2238,"ariaHidden":721},[720],[690,2240,2242,2245],{"className":2241},[725],[690,2243],{"className":2244,"style":1005},[729],[690,2246,1026],{"className":2247,"style":1041},[734,1009],[661,2249,2250,2251],{},"Somme = ",[690,2252,2254,2271],{"className":2253},[693],[690,2255,2257],{"className":2256},[697],[699,2258,2259],{"xmlns":701},[703,2260,2261,2269],{},[706,2262,2263,2265,2267],{},[815,2264,993],{},[709,2266,1535],{},[815,2268,1026],{},[713,2270,1645],{"encoding":715},[690,2272,2274,2292],{"className":2273,"ariaHidden":721},[720],[690,2275,2277,2280,2283,2286,2289],{"className":2276},[725],[690,2278],{"className":2279,"style":1655},[729],[690,2281,993],{"className":2282},[734,1009],[690,2284],{"className":2285,"style":1081},[1080],[690,2287,1535],{"className":2288},[1085],[690,2290],{"className":2291,"style":1081},[1080],[690,2293,2295,2298],{"className":2294},[725],[690,2296],{"className":2297,"style":1005},[729],[690,2299,1026],{"className":2300,"style":1041},[734,1009],[661,2302,2303,2304],{},"Retenue = ",[690,2305,2307,2324],{"className":2306},[693],[690,2308,2310],{"className":2309},[697],[699,2311,2312],{"xmlns":701},[703,2313,2314,2322],{},[706,2315,2316,2318,2320],{},[815,2317,993],{},[709,2319,711],{},[815,2321,1026],{},[713,2323,1064],{"encoding":715},[690,2325,2327,2345],{"className":2326,"ariaHidden":721},[720],[690,2328,2330,2333,2336,2339,2342],{"className":2329},[725],[690,2331],{"className":2332,"style":1005},[729],[690,2334,993],{"className":2335},[734,1009],[690,2337],{"className":2338,"style":1081},[1080],[690,2340,711],{"className":2341},[1085],[690,2343],{"className":2344,"style":1081},[1080],[690,2346,2348,2351],{"className":2347},[725],[690,2349],{"className":2350,"style":1005},[729],[690,2352,1026],{"className":2353,"style":1041},[734,1009],[674,2355,2356,2366,2376,2386],{},[658,2357,2358,2360,2362,2364],{},[679,2359,1987],{},[679,2361,1987],{},[679,2363,1987],{},[679,2365,1987],{},[658,2367,2368,2370,2372,2374],{},[679,2369,1987],{},[679,2371,1785],{},[679,2373,1785],{},[679,2375,1987],{},[658,2377,2378,2380,2382,2384],{},[679,2379,1785],{},[679,2381,1987],{},[679,2383,1785],{},[679,2385,1987],{},[658,2387,2388,2390,2392,2394],{},[679,2389,1785],{},[679,2391,1785],{},[679,2393,1987],{},[679,2395,2396],{},[602,2397,1785],{},[598,2399,2400,2401,2404,2405,617],{},"C'est ce circuit minimal, appelé ",[602,2402,2403],{},"demi-additionneur",", qu'on assemble pour\nconstruire l'additionneur complet d'un processeur. La logique booléenne n'est\ndonc pas qu'abstraite : elle est ",[602,2406,2407],{},"gravée dans le silicium",[593,2409,2411],{"id":2410},"pièges-courants","Pièges courants",[2142,2413,2414],{},[1839,2415,2416,2435,2460,2474],{},[1842,2417,2418,2419,639,2421,2423,2424,2427,2428,2430,2431,2434],{},"En Python, ",[636,2420,638],{},[636,2422,642],{}," prennent une ",[602,2425,2426],{},"majuscule initiale",". ",[636,2429,721],{},"\n(avec t minuscule) n'est ",[602,2432,2433],{},"pas"," une valeur valide.",[1842,2436,2437,2438,2440,2441,2444,2445,2448,2449,2452,2453,2456,2457,2459],{},"Ne pas confondre ",[636,2439,1737],{}," (affectation) et ",[636,2442,2443],{},"=="," (test d'égalité) : ",[636,2446,2447],{},"x = 5"," met 5\ndans ",[636,2450,2451],{},"x"," ; ",[636,2454,2455],{},"x == 5"," teste si ",[636,2458,2451],{}," vaut 5 et retourne un booléen.",[1842,2461,2462,2463,2466,2467,2470,2471,617],{},"Sans parenthèses, ",[636,2464,2465],{},"not a == b"," se lit ",[636,2468,2469],{},"not(a == b)",", pas ",[636,2472,2473],{},"(not a) == b",[1842,2475,2476,2477,1742,2480,1742,2483,2486,2487,2490,2491,1742,2493,1742,2495,2497],{},"Les opérateurs ",[636,2478,2479],{},"&",[636,2481,2482],{},"|",[636,2484,2485],{},"^"," existent aussi mais agissent ",[602,2488,2489],{},"bit à bit"," sur\ndes entiers — c'est différent de ",[636,2492,686],{},[636,2494,751],{},[636,2496,1510],{}," sur des booléens.",[593,2499,2501],{"id":2500},"pour-aller-plus-loin","Pour aller plus loin",[598,2503,2504,2505,1742,2507,639,2509,2511,2512,2515,2516,2519],{},"Toute fonction logique, aussi complexe soit-elle, peut être réécrite\nuniquement avec ",[636,2506,799],{},[636,2508,686],{},[636,2510,751],{}," (on parle d'",[602,2513,2514],{},"ensemble fonctionnellement\ncomplet","). En électronique, l'opérateur ",[636,2517,2518],{},"nand"," (NON-ET) suffit à lui seul à\ntout reconstruire — d'où son utilisation massive dans la conception des puces.",[2521,2522,2523],"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 .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}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 .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}",{"title":847,"searchDepth":880,"depth":880,"links":2525},[2526,2527,2528,2536,2538,2539,2540,2541,2542],{"id":595,"depth":880,"text":596},{"id":646,"depth":880,"text":647},{"id":955,"depth":880,"text":956,"children":2529},[2530,2532,2534],{"id":967,"depth":900,"text":2531},"and (ET logique)",{"id":1138,"depth":900,"text":2533},"or (OU logique)",{"id":1303,"depth":900,"text":2535},"not (NON logique)",{"id":1506,"depth":880,"text":2537},"Le ou exclusif — xor",{"id":1852,"depth":880,"text":1853},{"id":2014,"depth":880,"text":2015},{"id":2153,"depth":880,"text":2154},{"id":2410,"depth":880,"text":2411},{"id":2500,"depth":880,"text":2501},"Le calcul à deux états — vrai ou faux — qui structure toute condition et tout test en programmation.",null,"md",{},true,[2549,2553,2556],{"slug":1829,"kind":2550,"question":1835,"choices":2551,"correct":1447,"multi":2552,"explanation":847},"qcm",[686,751,1510,799],false,{"slug":1967,"kind":2550,"question":2554,"choices":2555,"correct":1785,"multi":2552,"explanation":847},"Que vaut not (True or False) ?",[638,642],{"slug":1988,"kind":2550,"question":2557,"choices":2558,"correct":1987,"multi":2552,"explanation":847},"Sans parenthèses, que vaut True or False and False (rappel : and est prioritaire sur or) ?",[638,642],{"title":279,"description":2543},"5uP-GwBvt02044m2-qUAT-95DiG_Ji3GQhhd7Xj3DPw",{"id":2562,"title":2563,"bo":2564,"body":2565,"description":3024,"eval":2544,"extension":2545,"labo":2544,"meta":3025,"navigation":2552,"path":3026,"quizzes":3027,"readingTime":853,"seo":3028,"stem":3029,"tp":2544,"__hash__":3030},"coursMemo\u002F1.nsi-1ere\u002Fpb-types-valeurs\u002F5.booleens.memo.md","Valeurs booléennes — l'essentiel",[588],{"type":590,"value":2566,"toc":3017},[2567,2571,2584,2588,2754,2758,2891,2893,2934,2938,3014],[593,2568,2570],{"id":2569},"en-une-phrase","En une phrase",[598,2572,959,2573,2576,2577,1742,2579,1742,2581,2583],{},[602,2574,2575],{},"valeur booléenne"," vaut vrai ou faux ; les opérateurs ",[636,2578,686],{},[636,2580,751],{},[636,2582,799],{},"\npermettent de combiner des conditions pour en faire des décisions.",[593,2585,2587],{"id":2586},"à-mémoriser","À mémoriser",[1839,2589,2590,2598,2722,2732],{},[1842,2591,2592,2593,639,2595,2597],{},"En Python : ",[636,2594,638],{},[636,2596,642],{}," (majuscule initiale obligatoire).",[1842,2599,2600,2601],{},"Tables de vérité élémentaires :\n",[1839,2602,2603,2668,2676,2710],{},[1842,2604,2605,2607,2608,2047,2611,639,2639,2667],{},[636,2606,2039],{}," : vrai ",[602,2609,2610],{},"uniquement si",[690,2612,2614,2627],{"className":2613},[693],[690,2615,2617],{"className":2616},[697],[699,2618,2619],{"xmlns":701},[703,2620,2621,2625],{},[706,2622,2623],{},[815,2624,993],{},[713,2626,993],{"encoding":715},[690,2628,2630],{"className":2629,"ariaHidden":721},[720],[690,2631,2633,2636],{"className":2632},[725],[690,2634],{"className":2635,"style":1005},[729],[690,2637,993],{"className":2638},[734,1009],[690,2640,2642,2655],{"className":2641},[693],[690,2643,2645],{"className":2644},[697],[699,2646,2647],{"xmlns":701},[703,2648,2649,2653],{},[706,2650,2651],{},[815,2652,1026],{},[713,2654,1026],{"encoding":715},[690,2656,2658],{"className":2657,"ariaHidden":721},[720],[690,2659,2661,2664],{"className":2660},[725],[690,2662],{"className":2663,"style":1005},[729],[690,2665,1026],{"className":2666,"style":1041},[734,1009]," sont vrais.",[1842,2669,2670,2607,2672,2675],{},[636,2671,2054],{},[602,2673,2674],{},"si au moins un"," des deux est vrai.",[1842,2677,2678,2681,2682,617],{},[636,2679,2680],{},"not A"," : inverse ",[690,2683,2685,2698],{"className":2684},[693],[690,2686,2688],{"className":2687},[697],[699,2689,2690],{"xmlns":701},[703,2691,2692,2696],{},[706,2693,2694],{},[815,2695,993],{},[713,2697,993],{"encoding":715},[690,2699,2701],{"className":2700,"ariaHidden":721},[720],[690,2702,2704,2707],{"className":2703},[725],[690,2705],{"className":2706,"style":1005},[729],[690,2708,993],{"className":2709},[734,1009],[1842,2711,2712,2714,2715,2718,2719,2675],{},[636,2713,2172],{}," (écrit ",[636,2716,2717],{},"A != B",") : vrai ",[602,2720,2721],{},"si exactement un",[1842,2723,2724,2725,2727,2728,2727,2730,617],{},"Priorité : ",[636,2726,799],{}," > ",[636,2729,686],{},[636,2731,751],{},[1842,2733,2734,2735,2737,2738,2740,2741,2743,2744,2746,2747,2740,2749,2743,2751,2753],{},"Évaluation ",[602,2736,2032],{}," (court-circuit) : ",[636,2739,2039],{}," n'évalue pas ",[636,2742,1026],{}," si ",[636,2745,993],{}," est faux ; ",[636,2748,2054],{},[636,2750,1026],{},[636,2752,993],{}," est vrai.",[593,2755,2757],{"id":2756},"à-savoir-reconnaître","À savoir reconnaître",[652,2759,2760,2770],{},[655,2761,2762],{},[658,2763,2764,2767],{},[661,2765,2766],{},"Situation",[661,2768,2769],{},"Action à mener",[674,2771,2772,2867,2878],{},[658,2773,2774,2806],{},[679,2775,2776,2777,2805],{},"Dresser une table de vérité à ",[690,2778,2780,2793],{"className":2779},[693],[690,2781,2783],{"className":2782},[697],[699,2784,2785],{"xmlns":701},[703,2786,2787,2791],{},[706,2788,2789],{},[815,2790,1413],{},[713,2792,1413],{"encoding":715},[690,2794,2796],{"className":2795,"ariaHidden":721},[720],[690,2797,2799,2802],{"className":2798},[725],[690,2800],{"className":2801,"style":831},[729],[690,2803,1413],{"className":2804},[734,1009]," variables",[679,2807,2808,2866],{},[690,2809,2811,2828],{"className":2810},[693],[690,2812,2814],{"className":2813},[697],[699,2815,2816],{"xmlns":701},[703,2817,2818,2826],{},[706,2819,2820],{},[1442,2821,2822,2824],{},[1445,2823,1447],{},[815,2825,1413],{},[713,2827,1452],{"encoding":715},[690,2829,2831],{"className":2830,"ariaHidden":721},[720],[690,2832,2834,2837],{"className":2833},[725],[690,2835],{"className":2836,"style":1462},[729],[690,2838,2840,2843],{"className":2839},[734],[690,2841,1447],{"className":2842},[734],[690,2844,2846],{"className":2845},[1472],[690,2847,2849],{"className":2848},[1476],[690,2850,2852],{"className":2851},[1480],[690,2853,2855],{"className":2854,"style":1462},[1484],[690,2856,2857,2860],{"style":1487},[690,2858],{"className":2859,"style":1492},[1491],[690,2861,2863],{"className":2862},[1496,1497,1498,1499],[690,2864,1413],{"className":2865},[734,1009,1499]," lignes, énumérer toutes les combinaisons.",[658,2868,2869,2872],{},[679,2870,2871],{},"Protéger un accès",[679,2873,2874,2877],{},[636,2875,2876],{},"if liste and liste[0] > 5:"," — court-circuit.",[658,2879,2880,2883],{},[679,2881,2882],{},"Addition binaire 1 bit",[679,2884,2885,2886,2888,2889,617],{},"somme = ",[636,2887,2172],{},", retenue = ",[636,2890,2039],{},[593,2892,2411],{"id":2410},[1839,2894,2895,2906,2915],{},[1842,2896,2897,2899,2900,2902,2903,2905],{},[636,2898,638],{}," \u002F ",[636,2901,642],{}," avec majuscule. ",[636,2904,721],{}," n'existe pas en Python.",[1842,2907,2908,2466,2910,2470,2913,617],{},[636,2909,2465],{},[636,2911,2912],{},"not (a == b)",[636,2914,2473],{},[1842,2916,2917,1742,2919,1742,2921,2923,2924,2926,2927,2929,2930,2929,2932,2497],{},[636,2918,2479],{},[636,2920,2482],{},[636,2922,2485],{}," opèrent ",[602,2925,2489],{}," sur des entiers, pas comme ",[636,2928,686],{},"\u002F",[636,2931,751],{},[636,2933,1510],{},[593,2935,2937],{"id":2936},"syntaxe-python","Syntaxe Python",[842,2939,2941],{"className":844,"code":2940,"language":846,"meta":847,"style":847},"True and False     # False\nTrue or False      # True\nnot True           # False\nA != B             # équivalent xor\nif liste and liste[0] > 5:\n    ...\n",[636,2942,2943,2954,2965,2974,2987,3008],{"__ignoreMap":847},[690,2944,2945,2947,2949,2951],{"class":852,"line":853},[690,2946,638],{"class":856},[690,2948,867],{"class":866},[690,2950,870],{"class":856},[690,2952,2953],{"class":876},"     # False\n",[690,2955,2956,2958,2960,2962],{"class":852,"line":880},[690,2957,638],{"class":856},[690,2959,889],{"class":866},[690,2961,870],{"class":856},[690,2963,2964],{"class":876},"      # True\n",[690,2966,2967,2969,2971],{"class":852,"line":900},[690,2968,799],{"class":866},[690,2970,909],{"class":856},[690,2972,2973],{"class":876},"           # False\n",[690,2975,2976,2979,2981,2984],{"class":852,"line":917},[690,2977,2978],{"class":860},"A ",[690,2980,1723],{"class":866},[690,2982,2983],{"class":860}," B             ",[690,2985,2986],{"class":876},"# équivalent xor\n",[690,2988,2990,2992,2994,2996,2998,3000,3002,3004,3006],{"class":852,"line":2989},5,[690,2991,1937],{"class":866},[690,2993,2093],{"class":860},[690,2995,686],{"class":866},[690,2997,2098],{"class":860},[690,2999,1987],{"class":856},[690,3001,2103],{"class":860},[690,3003,2106],{"class":866},[690,3005,2109],{"class":856},[690,3007,2112],{"class":860},[690,3009,3011],{"class":852,"line":3010},6,[690,3012,3013],{"class":856},"    ...\n",[2521,3015,3016],{},"html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sCsY4, html code.shiki .sCsY4{--shiki-light:#6A737D;--shiki-default:#6A737D;--shiki-dark:#6A737D}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}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":847,"searchDepth":880,"depth":880,"links":3018},[3019,3020,3021,3022,3023],{"id":2569,"depth":880,"text":2570},{"id":2586,"depth":880,"text":2587},{"id":2756,"depth":880,"text":2757},{"id":2410,"depth":880,"text":2411},{"id":2936,"depth":880,"text":2937},"Mémo de révision sur les opérateurs logiques et les tables de vérité.",{},"\u002Fnsi-1ere\u002Fpb-types-valeurs\u002Fbooleens.memo",[],{"title":2563,"description":3024},"1.nsi-1ere\u002Fpb-types-valeurs\u002F5.booleens.memo","30Sop2HhFOzYiDk72irvpMaoO1upyTiAoHYMVfu9rf4",{"id":3032,"title":3033,"body":3034,"description":3560,"extension":2545,"meta":3561,"navigation":2552,"path":3562,"seo":3563,"stem":3564,"__hash__":3565},"coursSlides\u002F1.nsi-1ere\u002Fpb-types-valeurs\u002F5.booleens.slides.md","Valeurs booléennes — diapositives",{"type":590,"value":3035,"toc":3558},[3036,3041,3044,3047,3051,3181,3183,3189,3239,3241,3246,3298,3300,3305,3329,3331,3337,3387,3391,3393,3397,3411,3417,3419,3423,3459,3470,3472,3476,3536,3544,3546,3550,3555],[3037,3038,3040],"h1",{"id":3039},"valeurs-booléennes","Valeurs booléennes",[598,3042,3043],{},"Le calcul à deux états : vrai ou faux.",[3045,3046],"hr",{},[3037,3048,3050],{"id":3049},"deux-valeurs-trois-opérateurs","Deux valeurs, trois opérateurs",[652,3052,3053,3065],{},[655,3054,3055],{},[658,3056,3057,3060,3062],{},[661,3058,3059],{},"Logique",[661,3061,666],{},[661,3063,3064],{},"Math",[674,3066,3067,3105,3143],{},[658,3068,3069,3071,3075],{},[679,3070,681],{},[679,3072,3073],{},[636,3074,686],{},[679,3076,3077],{},[690,3078,3080,3093],{"className":3079},[693],[690,3081,3083],{"className":3082},[697],[699,3084,3085],{"xmlns":701},[703,3086,3087,3091],{},[706,3088,3089],{},[709,3090,711],{},[713,3092,716],{"encoding":715},[690,3094,3096],{"className":3095,"ariaHidden":721},[720],[690,3097,3099,3102],{"className":3098},[725],[690,3100],{"className":3101,"style":730},[729],[690,3103,711],{"className":3104},[734],[658,3106,3107,3109,3113],{},[679,3108,746],{},[679,3110,3111],{},[636,3112,751],{},[679,3114,3115],{},[690,3116,3118,3131],{"className":3117},[693],[690,3119,3121],{"className":3120},[697],[699,3122,3123],{"xmlns":701},[703,3124,3125,3129],{},[706,3126,3127],{},[709,3128,768],{},[713,3130,771],{"encoding":715},[690,3132,3134],{"className":3133,"ariaHidden":721},[720],[690,3135,3137,3140],{"className":3136},[725],[690,3138],{"className":3139,"style":730},[729],[690,3141,768],{"className":3142},[734],[658,3144,3145,3147,3151],{},[679,3146,794],{},[679,3148,3149],{},[636,3150,799],{},[679,3152,3153],{},[690,3154,3156,3169],{"className":3155},[693],[690,3157,3159],{"className":3158},[697],[699,3160,3161],{"xmlns":701},[703,3162,3163,3167],{},[706,3164,3165],{},[815,3166,818],{"mathvariant":817},[713,3168,821],{"encoding":715},[690,3170,3172],{"className":3171,"ariaHidden":721},[720],[690,3173,3175,3178],{"className":3174},[725],[690,3176],{"className":3177,"style":831},[729],[690,3179,818],{"className":3180},[734],[3045,3182],{},[3037,3184,3186,3187],{"id":3185},"table-de-and","Table de ",[636,3188,686],{},[652,3190,3191,3201],{},[655,3192,3193],{},[658,3194,3195,3197,3199],{},[661,3196,993],{},[661,3198,1026],{},[661,3200,2039],{},[674,3202,3203,3212,3221,3229],{},[658,3204,3205,3208,3210],{},[679,3206,3207],{},"F",[679,3209,3207],{},[679,3211,3207],{},[658,3213,3214,3216,3219],{},[679,3215,3207],{},[679,3217,3218],{},"V",[679,3220,3207],{},[658,3222,3223,3225,3227],{},[679,3224,3218],{},[679,3226,3207],{},[679,3228,3207],{},[658,3230,3231,3233,3235],{},[679,3232,3218],{},[679,3234,3218],{},[679,3236,3237],{},[602,3238,3218],{},[3045,3240],{},[3037,3242,3186,3244],{"id":3243},"table-de-or",[636,3245,751],{},[652,3247,3248,3258],{},[655,3249,3250],{},[658,3251,3252,3254,3256],{},[661,3253,993],{},[661,3255,1026],{},[661,3257,2054],{},[674,3259,3260,3268,3278,3288],{},[658,3261,3262,3264,3266],{},[679,3263,3207],{},[679,3265,3207],{},[679,3267,3207],{},[658,3269,3270,3272,3274],{},[679,3271,3207],{},[679,3273,3218],{},[679,3275,3276],{},[602,3277,3218],{},[658,3279,3280,3282,3284],{},[679,3281,3218],{},[679,3283,3207],{},[679,3285,3286],{},[602,3287,3218],{},[658,3289,3290,3292,3294],{},[679,3291,3218],{},[679,3293,3218],{},[679,3295,3296],{},[602,3297,3218],{},[3045,3299],{},[3037,3301,3186,3303],{"id":3302},"table-de-not",[636,3304,799],{},[652,3306,3307,3315],{},[655,3308,3309],{},[658,3310,3311,3313],{},[661,3312,993],{},[661,3314,2680],{},[674,3316,3317,3323],{},[658,3318,3319,3321],{},[679,3320,3207],{},[679,3322,3218],{},[658,3324,3325,3327],{},[679,3326,3218],{},[679,3328,3207],{},[3045,3330],{},[3037,3332,3334,3336],{"id":3333},"xor-ou-exclusif",[636,3335,1510],{}," — ou exclusif",[652,3338,3339,3349],{},[655,3340,3341],{},[658,3342,3343,3345,3347],{},[661,3344,993],{},[661,3346,1026],{},[661,3348,2172],{},[674,3350,3351,3359,3369,3379],{},[658,3352,3353,3355,3357],{},[679,3354,3207],{},[679,3356,3207],{},[679,3358,3207],{},[658,3360,3361,3363,3365],{},[679,3362,3207],{},[679,3364,3218],{},[679,3366,3367],{},[602,3368,3218],{},[658,3370,3371,3373,3375],{},[679,3372,3218],{},[679,3374,3207],{},[679,3376,3377],{},[602,3378,3218],{},[658,3380,3381,3383,3385],{},[679,3382,3218],{},[679,3384,3218],{},[679,3386,3207],{},[598,3388,2592,3389,617],{},[636,3390,2717],{},[3045,3392],{},[3037,3394,3396],{"id":3395},"priorité-des-opérateurs","Priorité des opérateurs",[1870,3398,3399,3403,3407],{},[1842,3400,3401],{},[636,3402,799],{},[1842,3404,3405],{},[636,3406,686],{},[1842,3408,3409],{},[636,3410,751],{},[598,3412,3413,3414,617],{},"En cas de doute → ",[602,3415,3416],{},"parenthèses",[3045,3418],{},[3037,3420,3422],{"id":3421},"court-circuit-évaluation-séquentielle","Court-circuit (évaluation séquentielle)",[842,3424,3426],{"className":844,"code":3425,"language":846,"meta":847,"style":847},"if liste and liste[0] > 5:\n    print(\"OK\")\n",[636,3427,3428,3448],{"__ignoreMap":847},[690,3429,3430,3432,3434,3436,3438,3440,3442,3444,3446],{"class":852,"line":853},[690,3431,1937],{"class":866},[690,3433,2093],{"class":860},[690,3435,686],{"class":866},[690,3437,2098],{"class":860},[690,3439,1987],{"class":856},[690,3441,2103],{"class":860},[690,3443,2106],{"class":866},[690,3445,2109],{"class":856},[690,3447,2112],{"class":860},[690,3449,3450,3452,3454,3457],{"class":852,"line":880},[690,3451,2117],{"class":856},[690,3453,861],{"class":860},[690,3455,3456],{"class":2122},"\"OK\"",[690,3458,2126],{"class":860},[598,3460,2129,3461,3463,3464,3466,3467,3469],{},[636,3462,2132],{}," est vide → ",[636,3465,2139],{}," n'est ",[602,3468,2433],{}," évalué, donc pas d'erreur.",[3045,3471],{},[3037,3473,3475],{"id":3474},"application-addition-binaire","Application — addition binaire",[652,3477,3478,3492],{},[655,3479,3480],{},[658,3481,3482,3484,3486,3489],{},[661,3483,993],{},[661,3485,1026],{},[661,3487,3488],{},"Somme",[661,3490,3491],{},"Retenue",[674,3493,3494,3504,3514,3524],{},[658,3495,3496,3498,3500,3502],{},[679,3497,1987],{},[679,3499,1987],{},[679,3501,1987],{},[679,3503,1987],{},[658,3505,3506,3508,3510,3512],{},[679,3507,1987],{},[679,3509,1785],{},[679,3511,1785],{},[679,3513,1987],{},[658,3515,3516,3518,3520,3522],{},[679,3517,1785],{},[679,3519,1987],{},[679,3521,1785],{},[679,3523,1987],{},[658,3525,3526,3528,3530,3532],{},[679,3527,1785],{},[679,3529,1785],{},[679,3531,1987],{},[679,3533,3534],{},[602,3535,1785],{},[598,3537,2250,3538,2888,3540,1901,3542,617],{},[636,3539,2172],{},[636,3541,2039],{},[602,3543,2403],{},[3045,3545],{},[3037,3547,3549],{"id":3548},"à-retenir","À retenir",[598,3551,3552],{},[602,3553,3554],{},"Toute condition en programmation se ramène à une expression booléenne.\nComprendre la table de vérité, c'est comprendre la décision.",[2521,3556,3557],{},"html pre.shiki code .s8jYJ, html code.shiki .s8jYJ{--shiki-light:#D73A49;--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sxrX7, html code.shiki .sxrX7{--shiki-light:#24292E;--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}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":847,"searchDepth":880,"depth":880,"links":3559},[],"Deck pour la séance sur les opérateurs 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