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Web","\u002Fsnt-2nde\u002Fsb-web","0.snt-2nde\u002Fsb-web\u002F0.index",[41,42,46,50,54,58,62],{"title":37,"path":38,"stem":39},{"title":43,"path":44,"stem":45},"Histoire du Web","\u002Fsnt-2nde\u002Fsb-web\u002Fhistoire-web","0.snt-2nde\u002Fsb-web\u002F1.histoire-web",{"title":47,"path":48,"stem":49},"URL et hypertexte","\u002Fsnt-2nde\u002Fsb-web\u002Furl-hypertexte","0.snt-2nde\u002Fsb-web\u002F2.url-hypertexte",{"title":51,"path":52,"stem":53},"HTML et CSS — le contenu et la présentation","\u002Fsnt-2nde\u002Fsb-web\u002Fhtml-css","0.snt-2nde\u002Fsb-web\u002F3.html-css",{"title":55,"path":56,"stem":57},"Client-serveur et requêtes HTTP","\u002Fsnt-2nde\u002Fsb-web\u002Fclient-serveur-http","0.snt-2nde\u002Fsb-web\u002F4.client-serveur-http",{"title":59,"path":60,"stem":61},"Moteurs de recherche","\u002Fsnt-2nde\u002Fsb-web\u002Fmoteurs-recherche","0.snt-2nde\u002Fsb-web\u002F5.moteurs-recherche",{"title":63,"path":64,"stem":65},"Sécurité du navigateur et notions juridiques","\u002Fsnt-2nde\u002Fsb-web\u002Fsecurite-droits","0.snt-2nde\u002Fsb-web\u002F6.securite-droits",{"title":67,"path":68,"stem":69,"children":70},"Les réseaux sociaux","\u002Fsnt-2nde\u002Fsc-reseaux-sociaux","0.snt-2nde\u002Fsc-reseaux-sociaux\u002F0.index",[71,72,76,80,84,88],{"title":67,"path":68,"stem":69},{"title":73,"path":74,"stem":75},"Panorama des réseaux sociaux","\u002Fsnt-2nde\u002Fsc-reseaux-sociaux\u002Fpanorama-rs","0.snt-2nde\u002Fsc-reseaux-sociaux\u002F1.panorama-rs",{"title":77,"path":78,"stem":79},"Identité numérique et authentification","\u002Fsnt-2nde\u002Fsc-reseaux-sociaux\u002Fidentite-numerique","0.snt-2nde\u002Fsc-reseaux-sociaux\u002F2.identite-numerique",{"title":81,"path":82,"stem":83},"Le modèle économique des réseaux sociaux","\u002Fsnt-2nde\u002Fsc-reseaux-sociaux\u002Fmodele-economique","0.snt-2nde\u002Fsc-reseaux-sociaux\u002F3.modele-economique",{"title":85,"path":86,"stem":87},"Petit monde et graphes","\u002Fsnt-2nde\u002Fsc-reseaux-sociaux\u002Fpetit-monde-graphes","0.snt-2nde\u002Fsc-reseaux-sociaux\u002F4.petit-monde-graphes",{"title":89,"path":90,"stem":91},"La cyberviolence","\u002Fsnt-2nde\u002Fsc-reseaux-sociaux\u002Fcyberviolence","0.snt-2nde\u002Fsc-reseaux-sociaux\u002F5.cyberviolence",{"title":93,"path":94,"stem":95,"children":96},"Les données structurées et leur traitement","\u002Fsnt-2nde\u002Fsd-donnees-structurees","0.snt-2nde\u002Fsd-donnees-structurees\u002F0.index",[97,98,102,106,110,114],{"title":93,"path":94,"stem":95},{"title":99,"path":100,"stem":101},"Données et formats","\u002Fsnt-2nde\u002Fsd-donnees-structurees\u002Fdonnees-formats","0.snt-2nde\u002Fsd-donnees-structurees\u002F1.donnees-formats",{"title":103,"path":104,"stem":105},"Données 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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 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 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":129,"bo":587,"body":589,"description":2101,"eval":2102,"extension":2103,"labo":2102,"meta":2104,"navigation":1636,"path":130,"quizzes":2105,"readingTime":1619,"seo":2112,"stem":131,"tp":2102,"__hash__":2113},"cours\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F2.trame-nmea.md",[588],"SE05",{"type":590,"value":591,"toc":2091},"minimark",[592,597,610,613,617,630,633,662,668,672,685,695,702,790,797,821,825,843,1182,1188,1378,1383,1560,1567,1577,1581,1588,1609,1747,1750,1831,1943,1965,1969,1987,1994,1998,2001,2064,2067,2077,2081,2087],[593,594,596],"h2",{"id":595},"introduction","Introduction",[598,599,600,601,605,606,609],"p",{},"Le récepteur GPS de votre téléphone ne se contente pas de calculer votre\nposition : il la ",[602,603,604],"strong",{},"publie"," ensuite à toutes les applications qui ont besoin de\nla connaître. Mais sous quelle forme ? Comment cette suite de mesures\nsatellites devient-elle « 48,8566° N, 2,3522° E » ? La réponse passe par un\nprotocole textuel des années 1980, étonnamment encore en service aujourd'hui :\nle ",[602,607,608],{},"NMEA 0183",".",[611,612],"bo-ref",{"code":588},[593,614,616],{"id":615},"un-standard-maritime-devenu-universel","Un standard maritime devenu universel",[598,618,619,620,624,625,629],{},"NMEA est l'acronyme de la ",[621,622,623],"em",{},"National Marine Electronics Association",", qui a\ndéfini ce protocole pour faire dialoguer entre eux les équipements\nélectroniques des navires : sonde, gouvernail automatique, traceur de cartes,\nrécepteur GPS… La version ",[626,627,628],"code",{},"0183"," désigne une norme publiée en 1983, encore\nlargement utilisée.",[598,631,632],{},"Ce qu'il faut en retenir pour SNT :",[634,635,636,644,655],"ul",{},[637,638,639,640,643],"li",{},"Le NMEA 0183 est ",[602,641,642],{},"textuel"," — il transmet des chaînes de caractères ASCII,\nlisibles à l'œil nu.",[637,645,646,647,650,651,654],{},"Chaque message est une ",[602,648,649],{},"trame"," : une ligne autonome qui commence par ",[626,652,653],{},"$","\net se termine par un saut de ligne.",[637,656,657,658,661],{},"Chaque trame contient des ",[602,659,660],{},"champs séparés par des virgules",", comme un\nfichier CSV.",[663,664,665],"note",{},[598,666,667],{},"Bien que conçu pour la marine, le NMEA 0183 est devenu le langage commun de\nquasiment tous les récepteurs GNSS du monde. C'est ce que produisent les\nmodules GPS qu'on trouve dans les Arduino, les drones, les anciens GPS de\nvoiture, et même beaucoup de smartphones en interne.",[593,669,671],{"id":670},"anatomie-dune-trame-gga","Anatomie d'une trame GGA",[598,673,674,675,680,681,684],{},"La trame la plus courante est la trame ",[602,676,677],{},[626,678,679],{},"$GPGGA"," (",[621,682,683],{},"Global Positioning\nSystem Fix Data","). Elle donne la position calculée à un instant précis. Voici\nun exemple réel :",[686,687,693],"pre",{"className":688,"code":690,"language":691,"meta":692},[689],"language-text","$GPGGA,123519,4807.038,N,01131.000,E,1,08,0.9,545.4,M,46.9,M,,*47\n","text","",[626,694,690],{"__ignoreMap":692},[598,696,697,698,701],{},"À première vue, illisible. Mais l'œil s'y fait vite : il suffit de repérer\n",[602,699,700],{},"les champs principaux"," que vous avez besoin de savoir reconnaître.",[703,704,705,721],"table",{},[706,707,708],"thead",{},[709,710,711,715,718],"tr",{},[712,713,714],"th",{},"Champ",[712,716,717],{},"Valeur",[712,719,720],{},"Signification",[722,723,724,738,751,764,777],"tbody",{},[709,725,726,730,735],{},[727,728,729],"td",{},"heure UTC",[727,731,732],{},[626,733,734],{},"123519",[727,736,737],{},"12h 35min 19s",[709,739,740,743,748],{},[727,741,742],{},"latitude",[727,744,745],{},[626,746,747],{},"4807.038",[727,749,750],{},"48° 07,038′",[709,752,753,756,761],{},[727,754,755],{},"hémisphère",[727,757,758],{},[626,759,760],{},"N",[727,762,763],{},"Nord",[709,765,766,769,774],{},[727,767,768],{},"longitude",[727,770,771],{},[626,772,773],{},"01131.000",[727,775,776],{},"011° 31,000′",[709,778,779,782,787],{},[727,780,781],{},"méridien",[727,783,784],{},[626,785,786],{},"E",[727,788,789],{},"Est",[598,791,792,793,796],{},"C'est tout ce qu'il faut viser : être capable de pointer dans une trame\n",[602,794,795],{},"où sont"," la latitude, l'hémisphère, la longitude, le méridien et l'heure.\nLa trame contient d'autres informations techniques (qualité du fix, nombre\nde satellites, altitude, vérification…), regroupées dans la note ci-dessous\npour qui veut creuser.",[798,799,803,809],"self-eval-qcm",{"correct":800,"explanation":801,"slug":802},"1","Le champ heure se lit HHMMSS — 12h 35min 19s.","trame-nmea-c1",[804,805,806],"template",{"v-slot:question":692},[598,807,808],{},"Dans la trame ci-dessus, à quelle heure UTC la position a-t-elle été mesurée ?",[804,810,811],{"v-slot:choices":692},[634,812,813,816,818],{},[637,814,815],{},"1h 23min 51s",[637,817,737],{},[637,819,820],{},"13h 25min 19s",[593,822,824],{"id":823},"du-format-nmea-aux-degrés-décimaux","Du format NMEA aux degrés décimaux",[598,826,827,828,831,832,680,835,838,839,842],{},"Les coordonnées NMEA ne sont ",[602,829,830],{},"pas"," en degrés décimaux : elles sont au format\n",[602,833,834],{},"degrés-minutes",[626,836,837],{},"DDMM.MMMM"," pour la latitude, ",[626,840,841],{},"DDDMM.MMMM"," pour la\nlongitude). Pour les convertir en degrés décimaux, qu'utilisent la plupart des\napplications de cartographie, on applique :",[844,845,848],"span",{"className":846},[847],"katex-display",[844,849,852,930],{"className":850},[851],"katex",[844,853,856],{"className":854},[855],"katex-mathml",[857,858,861],"math",{"xmlns":859,"display":860},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[862,863,864,925],"semantics",{},[865,866,867,896,899,912,915],"mrow",{},[865,868,869,873,884,887,893],{},[870,871,872],"mtext",{},"degr",[874,875,877,880],"mover",{"accent":876},"true",[870,878,879],{},"e",[881,882,883],"mo",{},"ˊ",[870,885,886],{},"s d",[874,888,889,891],{"accent":876},[870,890,879],{},[881,892,883],{},[870,894,895],{},"cimaux",[881,897,898],{},"=",[865,900,901,903,909],{},[870,902,872],{},[874,904,905,907],{"accent":876},[870,906,879],{},[881,908,883],{},[870,910,911],{},"s entiers",[881,913,914],{},"+",[916,917,918,921],"mfrac",{},[870,919,920],{},"minutes",[922,923,924],"mn",{},"60",[926,927,929],"annotation",{"encoding":928},"application\u002Fx-tex","\\text{degrés décimaux} = \\text{degrés entiers} + \\frac{\\text{minutes}}{60}",[844,931,934,1040,1097],{"className":932,"ariaHidden":876},[933],"katex-html",[844,935,938,943,1028,1033,1037],{"className":936},[937],"base",[844,939],{"className":940,"style":942},[941],"strut","height:0.8889em;vertical-align:-0.1944em;",[844,944,947,950,991,994,1025],{"className":945},[946,691],"mord",[844,948,872],{"className":949},[946],[844,951,954],{"className":952},[946,953],"accent",[844,955,958],{"className":956},[957],"vlist-t",[844,959,962],{"className":960},[961],"vlist-r",[844,963,967,978],{"className":964,"style":966},[965],"vlist","height:0.6944em;",[844,968,970,975],{"style":969},"top:-3em;",[844,971],{"className":972,"style":974},[973],"pstrut","height:3em;",[844,976,879],{"className":977},[946],[844,979,980,983],{"style":969},[844,981],{"className":982,"style":974},[973],[844,984,988],{"className":985,"style":987},[986],"accent-body","left:-0.25em;",[844,989,883],{"className":990},[946],[844,992,886],{"className":993},[946],[844,995,997],{"className":996},[946,953],[844,998,1000],{"className":999},[957],[844,1001,1003],{"className":1002},[961],[844,1004,1006,1014],{"className":1005,"style":966},[965],[844,1007,1008,1011],{"style":969},[844,1009],{"className":1010,"style":974},[973],[844,1012,879],{"className":1013},[946],[844,1015,1016,1019],{"style":969},[844,1017],{"className":1018,"style":974},[973],[844,1020,1022],{"className":1021,"style":987},[986],[844,1023,883],{"className":1024},[946],[844,1026,895],{"className":1027},[946],[844,1029],{"className":1030,"style":1032},[1031],"mspace","margin-right:0.2778em;",[844,1034,898],{"className":1035},[1036],"mrel",[844,1038],{"className":1039,"style":1032},[1031],[844,1041,1043,1046,1086,1090,1094],{"className":1042},[937],[844,1044],{"className":1045,"style":942},[941],[844,1047,1049,1052,1083],{"className":1048},[946,691],[844,1050,872],{"className":1051},[946],[844,1053,1055],{"className":1054},[946,953],[844,1056,1058],{"className":1057},[957],[844,1059,1061],{"className":1060},[961],[844,1062,1064,1072],{"className":1063,"style":966},[965],[844,1065,1066,1069],{"style":969},[844,1067],{"className":1068,"style":974},[973],[844,1070,879],{"className":1071},[946],[844,1073,1074,1077],{"style":969},[844,1075],{"className":1076,"style":974},[973],[844,1078,1080],{"className":1079,"style":987},[986],[844,1081,883],{"className":1082},[946],[844,1084,911],{"className":1085},[946],[844,1087],{"className":1088,"style":1089},[1031],"margin-right:0.2222em;",[844,1091,914],{"className":1092},[1093],"mbin",[844,1095],{"className":1096,"style":1089},[1031],[844,1098,1100,1104],{"className":1099},[937],[844,1101],{"className":1102,"style":1103},[941],"height:2.0309em;vertical-align:-0.686em;",[844,1105,1107,1112,1178],{"className":1106},[946],[844,1108],{"className":1109},[1110,1111],"mopen","nulldelimiter",[844,1113,1115],{"className":1114},[916],[844,1116,1119,1169],{"className":1117},[957,1118],"vlist-t2",[844,1120,1122,1164],{"className":1121},[961],[844,1123,1126,1138,1149],{"className":1124,"style":1125},[965],"height:1.3449em;",[844,1127,1129,1132],{"style":1128},"top:-2.314em;",[844,1130],{"className":1131,"style":974},[973],[844,1133,1135],{"className":1134},[946],[844,1136,924],{"className":1137},[946],[844,1139,1141,1144],{"style":1140},"top:-3.23em;",[844,1142],{"className":1143,"style":974},[973],[844,1145],{"className":1146,"style":1148},[1147],"frac-line","border-bottom-width:0.04em;",[844,1150,1152,1155],{"style":1151},"top:-3.677em;",[844,1153],{"className":1154,"style":974},[973],[844,1156,1158],{"className":1157},[946],[844,1159,1161],{"className":1160},[946,691],[844,1162,920],{"className":1163},[946],[844,1165,1168],{"className":1166},[1167],"vlist-s","​",[844,1170,1172],{"className":1171},[961],[844,1173,1176],{"className":1174,"style":1175},[965],"height:0.686em;",[844,1177],{},[844,1179],{"className":1180},[1181,1111],"mclose",[598,1183,1184,1185,1187],{},"Reprenons la latitude ",[626,1186,747],{}," :",[634,1189,1190,1196,1202],{},[637,1191,1192,1193],{},"degrés entiers : ",[602,1194,1195],{},"48",[637,1197,1198,1199],{},"minutes : ",[602,1200,1201],{},"07,038",[637,1203,1204,1205],{},"conversion : ",[844,1206,1208,1245],{"className":1207},[851],[844,1209,1211],{"className":1210},[855],[857,1212,1213],{"xmlns":859},[862,1214,1215,1242],{},[865,1216,1217,1219,1221,1232,1234,1237],{},[922,1218,1195],{},[881,1220,914],{},[1222,1223,1225],"mstyle",{"scriptlevel":1224,"displaystyle":876},"0",[916,1226,1227,1230],{},[922,1228,1229],{},"7,038",[922,1231,924],{},[881,1233,898],{},[922,1235,1236],{},"48,1173",[1238,1239,1241],"mi",{"mathvariant":1240},"normal","°",[926,1243,1244],{"encoding":928},"48 + \\dfrac{7{,}038}{60} = 48{,}1173°",[844,1246,1248,1267,1359],{"className":1247,"ariaHidden":876},[933],[844,1249,1251,1255,1258,1261,1264],{"className":1250},[937],[844,1252],{"className":1253,"style":1254},[941],"height:0.7278em;vertical-align:-0.0833em;",[844,1256,1195],{"className":1257},[946],[844,1259],{"className":1260,"style":1089},[1031],[844,1262,914],{"className":1263},[1093],[844,1265],{"className":1266,"style":1089},[1031],[844,1268,1270,1274,1350,1353,1356],{"className":1269},[937],[844,1271],{"className":1272,"style":1273},[941],"height:2.0074em;vertical-align:-0.686em;",[844,1275,1277,1280,1347],{"className":1276},[946],[844,1278],{"className":1279},[1110,1111],[844,1281,1283],{"className":1282},[916],[844,1284,1286,1339],{"className":1285},[957,1118],[844,1287,1289,1336],{"className":1288},[961],[844,1290,1293,1304,1312],{"className":1291,"style":1292},[965],"height:1.3214em;",[844,1294,1295,1298],{"style":1128},[844,1296],{"className":1297,"style":974},[973],[844,1299,1301],{"className":1300},[946],[844,1302,924],{"className":1303},[946],[844,1305,1306,1309],{"style":1140},[844,1307],{"className":1308,"style":974},[973],[844,1310],{"className":1311,"style":1148},[1147],[844,1313,1314,1317],{"style":1151},[844,1315],{"className":1316,"style":974},[973],[844,1318,1320,1324,1332],{"className":1319},[946],[844,1321,1323],{"className":1322},[946],"7",[844,1325,1327],{"className":1326},[946],[844,1328,1331],{"className":1329},[1330],"mpunct",",",[844,1333,1335],{"className":1334},[946],"038",[844,1337,1168],{"className":1338},[1167],[844,1340,1342],{"className":1341},[961],[844,1343,1345],{"className":1344,"style":1175},[965],[844,1346],{},[844,1348],{"className":1349},[1181,1111],[844,1351],{"className":1352,"style":1032},[1031],[844,1354,898],{"className":1355},[1036],[844,1357],{"className":1358,"style":1032},[1031],[844,1360,1362,1365,1368,1374],{"className":1361},[937],[844,1363],{"className":1364,"style":942},[941],[844,1366,1195],{"className":1367},[946],[844,1369,1371],{"className":1370},[946],[844,1372,1331],{"className":1373},[1330],[844,1375,1377],{"className":1376},[946],"1173°",[598,1379,1380,1381,1187],{},"Et la longitude ",[626,1382,773],{},[634,1384,1385,1390,1395],{},[637,1386,1192,1387],{},[602,1388,1389],{},"011",[637,1391,1198,1392],{},[602,1393,1394],{},"31,000",[637,1396,1204,1397],{},[844,1398,1400,1432],{"className":1399},[851],[844,1401,1403],{"className":1402},[855],[857,1404,1405],{"xmlns":859},[862,1406,1407,1429],{},[865,1408,1409,1412,1414,1422,1424,1427],{},[922,1410,1411],{},"11",[881,1413,914],{},[1222,1415,1416],{"scriptlevel":1224,"displaystyle":876},[916,1417,1418,1420],{},[922,1419,1394],{},[922,1421,924],{},[881,1423,898],{},[922,1425,1426],{},"11,5167",[1238,1428,1241],{"mathvariant":1240},[926,1430,1431],{"encoding":928},"11 + \\dfrac{31{,}000}{60} = 11{,}5167°",[844,1433,1435,1453,1541],{"className":1434,"ariaHidden":876},[933],[844,1436,1438,1441,1444,1447,1450],{"className":1437},[937],[844,1439],{"className":1440,"style":1254},[941],[844,1442,1411],{"className":1443},[946],[844,1445],{"className":1446,"style":1089},[1031],[844,1448,914],{"className":1449},[1093],[844,1451],{"className":1452,"style":1089},[1031],[844,1454,1456,1459,1532,1535,1538],{"className":1455},[937],[844,1457],{"className":1458,"style":1273},[941],[844,1460,1462,1465,1529],{"className":1461},[946],[844,1463],{"className":1464},[1110,1111],[844,1466,1468],{"className":1467},[916],[844,1469,1471,1521],{"className":1470},[957,1118],[844,1472,1474,1518],{"className":1473},[961],[844,1475,1477,1488,1496],{"className":1476,"style":1292},[965],[844,1478,1479,1482],{"style":1128},[844,1480],{"className":1481,"style":974},[973],[844,1483,1485],{"className":1484},[946],[844,1486,924],{"className":1487},[946],[844,1489,1490,1493],{"style":1140},[844,1491],{"className":1492,"style":974},[973],[844,1494],{"className":1495,"style":1148},[1147],[844,1497,1498,1501],{"style":1151},[844,1499],{"className":1500,"style":974},[973],[844,1502,1504,1508,1514],{"className":1503},[946],[844,1505,1507],{"className":1506},[946],"31",[844,1509,1511],{"className":1510},[946],[844,1512,1331],{"className":1513},[1330],[844,1515,1517],{"className":1516},[946],"000",[844,1519,1168],{"className":1520},[1167],[844,1522,1524],{"className":1523},[961],[844,1525,1527],{"className":1526,"style":1175},[965],[844,1528],{},[844,1530],{"className":1531},[1181,1111],[844,1533],{"className":1534,"style":1032},[1031],[844,1536,898],{"className":1537},[1036],[844,1539],{"className":1540,"style":1032},[1031],[844,1542,1544,1547,1550,1556],{"className":1543},[937],[844,1545],{"className":1546,"style":942},[941],[844,1548,1411],{"className":1549},[946],[844,1551,1553],{"className":1552},[946],[844,1554,1331],{"className":1555},[1330],[844,1557,1559],{"className":1558},[946],"5167°",[598,1561,1562,1563,1566],{},"La position décodée est donc : ",[602,1564,1565],{},"48,1173° N, 11,5167° E"," — ce qui place le\nrécepteur quelque part à Munich, en Allemagne.",[1568,1569,1570],"tip",{},[598,1571,1572,1573,1576],{},"Pour vérifier rapidement, copiez ",[626,1574,1575],{},"48.1173, 11.5167"," dans la barre de\nrecherche d'une carte en ligne. Le point bleu apparaîtra au cœur de la\ncapitale bavaroise.",[593,1578,1580],{"id":1579},"décoder-à-la-main-ou-en-pseudo-code","Décoder, à la main ou en pseudo-code",[598,1582,1583,1584,1587],{},"Décoder une trame, ce n'est rien d'autre que ",[602,1585,1586],{},"découper la chaîne autour\ndes virgules"," puis lire les morceaux dans l'ordre. À la main, vous suivez la\nligne du regard et vous numérotez les champs. En pseudo-code Python, l'idée\ns'écrit ainsi :",[663,1589,1590],{},[598,1591,1592,1593,1596,1597,1600,1601,1604,1605,1608],{},"Le bloc ci-dessous est du ",[602,1594,1595],{},"pseudo-code Python"," : la fonction\n",[626,1598,1599],{},"decouper_autour_des_virgules"," n'existe pas sous ce nom et n'est pas\nexécutable telle quelle. En vraie syntaxe, on appellerait la méthode\n",[626,1602,1603],{},"split(\",\")"," sur la chaîne. Ce qui compte ici est la ",[602,1606,1607],{},"logique"," : « je\ndécoupe, puis je lis le bon champ ».",[686,1610,1614],{"className":1611,"code":1612,"language":1613,"meta":692,"style":692},"language-python shiki shiki-themes github-light github-light github-dark","trame = \"$GPGGA,123519,4807.038,N,01131.000,E,1,08,0.9,545.4,M,46.9,M,,*47\"\n\nchamps = decouper_autour_des_virgules(trame)\n\nheure       = champs[1]   # \"123519\"\nlatitude    = champs[2]   # \"4807.038\"\nhemisphere  = champs[3]   # \"N\"\nlongitude   = champs[4]   # \"01131.000\"\nmeridien    = champs[5]   # \"E\"\n","python",[626,1615,1616,1631,1638,1649,1654,1675,1693,1711,1729],{"__ignoreMap":692},[844,1617,1620,1624,1627],{"class":1618,"line":1619},"line",1,[844,1621,1623],{"class":1622},"sxrX7","trame ",[844,1625,898],{"class":1626},"s8jYJ",[844,1628,1630],{"class":1629},"sIIMD"," \"$GPGGA,123519,4807.038,N,01131.000,E,1,08,0.9,545.4,M,46.9,M,,*47\"\n",[844,1632,1634],{"class":1618,"line":1633},2,[844,1635,1637],{"emptyLinePlaceholder":1636},true,"\n",[844,1639,1641,1644,1646],{"class":1618,"line":1640},3,[844,1642,1643],{"class":1622},"champs ",[844,1645,898],{"class":1626},[844,1647,1648],{"class":1622}," decouper_autour_des_virgules(trame)\n",[844,1650,1652],{"class":1618,"line":1651},4,[844,1653,1637],{"emptyLinePlaceholder":1636},[844,1655,1657,1660,1662,1665,1668,1671],{"class":1618,"line":1656},5,[844,1658,1659],{"class":1622},"heure       ",[844,1661,898],{"class":1626},[844,1663,1664],{"class":1622}," champs[",[844,1666,800],{"class":1667},"sBjJW",[844,1669,1670],{"class":1622},"]   ",[844,1672,1674],{"class":1673},"sCsY4","# \"123519\"\n",[844,1676,1678,1681,1683,1685,1688,1690],{"class":1618,"line":1677},6,[844,1679,1680],{"class":1622},"latitude    ",[844,1682,898],{"class":1626},[844,1684,1664],{"class":1622},[844,1686,1687],{"class":1667},"2",[844,1689,1670],{"class":1622},[844,1691,1692],{"class":1673},"# \"4807.038\"\n",[844,1694,1696,1699,1701,1703,1706,1708],{"class":1618,"line":1695},7,[844,1697,1698],{"class":1622},"hemisphere  ",[844,1700,898],{"class":1626},[844,1702,1664],{"class":1622},[844,1704,1705],{"class":1667},"3",[844,1707,1670],{"class":1622},[844,1709,1710],{"class":1673},"# \"N\"\n",[844,1712,1714,1717,1719,1721,1724,1726],{"class":1618,"line":1713},8,[844,1715,1716],{"class":1622},"longitude   ",[844,1718,898],{"class":1626},[844,1720,1664],{"class":1622},[844,1722,1723],{"class":1667},"4",[844,1725,1670],{"class":1622},[844,1727,1728],{"class":1673},"# \"01131.000\"\n",[844,1730,1732,1735,1737,1739,1742,1744],{"class":1618,"line":1731},9,[844,1733,1734],{"class":1622},"meridien    ",[844,1736,898],{"class":1626},[844,1738,1664],{"class":1622},[844,1740,1741],{"class":1667},"5",[844,1743,1670],{"class":1622},[844,1745,1746],{"class":1673},"# \"E\"\n",[598,1748,1749],{},"Pour la conversion en degrés décimaux, le travail se fait en français aussi\nbien qu'en code :",[1751,1752,1753],"blockquote",{},[598,1754,1755,1756,1759,1760,1763,1764,609],{},"On prend les ",[602,1757,1758],{},"deux premiers caractères"," de la latitude pour les degrés,\npuis ",[602,1761,1762],{},"tout ce qui suit"," pour les minutes. On applique la formule\n",[844,1765,1767,1792],{"className":1766},[851],[844,1768,1770],{"className":1769},[855],[857,1771,1772],{"xmlns":859},[862,1773,1774,1789],{},[865,1775,1776,1779,1781,1784,1787],{},[1238,1777,1778],{},"D",[881,1780,914],{},[1238,1782,1783],{},"M",[1238,1785,1786],{"mathvariant":1240},"\u002F",[922,1788,924],{},[926,1790,1791],{"encoding":928},"D + M\u002F60",[844,1793,1795,1816],{"className":1794,"ariaHidden":876},[933],[844,1796,1798,1802,1807,1810,1813],{"className":1797},[937],[844,1799],{"className":1800,"style":1801},[941],"height:0.7667em;vertical-align:-0.0833em;",[844,1803,1778],{"className":1804,"style":1806},[946,1805],"mathnormal","margin-right:0.0278em;",[844,1808],{"className":1809,"style":1089},[1031],[844,1811,914],{"className":1812},[1093],[844,1814],{"className":1815,"style":1089},[1031],[844,1817,1819,1823,1827],{"className":1818},[937],[844,1820],{"className":1821,"style":1822},[941],"height:1em;vertical-align:-0.25em;",[844,1824,1783],{"className":1825,"style":1826},[946,1805],"margin-right:0.109em;",[844,1828,1830],{"className":1829},[946],"\u002F60",[598,1832,1833,1834,1836,1837,1839,1840,1843,1844,1942],{},"Sur ",[626,1835,747],{}," : les deux premiers caractères sont ",[626,1838,1195],{},", le reste est\n",[626,1841,1842],{},"07.038",". Donc ",[844,1845,1847,1875],{"className":1846},[851],[844,1848,1850],{"className":1849},[855],[857,1851,1852],{"xmlns":859},[862,1853,1854,1872],{},[865,1855,1856,1858,1860,1862,1864,1866,1868,1870],{},[922,1857,1195],{},[881,1859,914],{},[922,1861,1229],{},[1238,1863,1786],{"mathvariant":1240},[922,1865,924],{},[881,1867,898],{},[922,1869,1236],{},[1238,1871,1241],{"mathvariant":1240},[926,1873,1874],{"encoding":928},"48 + 7{,}038\u002F60 = 48{,}1173°",[844,1876,1878,1896,1924],{"className":1877,"ariaHidden":876},[933],[844,1879,1881,1884,1887,1890,1893],{"className":1880},[937],[844,1882],{"className":1883,"style":1254},[941],[844,1885,1195],{"className":1886},[946],[844,1888],{"className":1889,"style":1089},[1031],[844,1891,914],{"className":1892},[1093],[844,1894],{"className":1895,"style":1089},[1031],[844,1897,1899,1902,1905,1911,1915,1918,1921],{"className":1898},[937],[844,1900],{"className":1901,"style":1822},[941],[844,1903,1323],{"className":1904},[946],[844,1906,1908],{"className":1907},[946],[844,1909,1331],{"className":1910},[1330],[844,1912,1914],{"className":1913},[946],"038\u002F60",[844,1916],{"className":1917,"style":1032},[1031],[844,1919,898],{"className":1920},[1036],[844,1922],{"className":1923,"style":1032},[1031],[844,1925,1927,1930,1933,1939],{"className":1926},[937],[844,1928],{"className":1929,"style":942},[941],[844,1931,1195],{"className":1932},[946],[844,1934,1936],{"className":1935},[946],[844,1937,1331],{"className":1938},[1330],[844,1940,1377],{"className":1941},[946],". Aucun outil informatique\nparticulier n'est requis pour faire ce calcul.",[798,1944,1947,1952],{"correct":800,"explanation":1945,"slug":1946},"5030.000 = 50° + 30 minutes \u002F 60 = 50 + 0,5 = 50,5°.","trame-nmea-c2",[804,1948,1949],{"v-slot:question":692},[598,1950,1951],{},"Si une trame indique une latitude de '5030.000' Nord, à combien de degrés décimaux cela correspond-il ?",[804,1953,1954],{"v-slot:choices":692},[634,1955,1956,1959,1962],{},[637,1957,1958],{},"50°",[637,1960,1961],{},"50,5°",[637,1963,1964],{},"50,8333°",[593,1966,1968],{"id":1967},"le-checksum-gardien-de-lintégrité","Le checksum, gardien de l'intégrité",[598,1970,1971,1972,1975,1976,1979,1980,1982,1983,1986],{},"Vous avez peut-être remarqué le ",[626,1973,1974],{},"*47"," à la fin de la trame. C'est un\n",[602,1977,1978],{},"checksum"," : un petit code de vérification qui permet au récepteur de\ndétecter une éventuelle corruption en transmission. Il est calculé par XOR de\ntous les caractères entre ",[626,1981,653],{}," et ",[626,1984,1985],{},"*",", et écrit en hexadécimal.",[598,1988,1989,1990,1993],{},"En pratique, vous n'avez pas à le calculer à la main : les bibliothèques le\nfont pour vous. Mais sa présence rappelle un principe général de tout\nprotocole de communication numérique : ",[602,1991,1992],{},"on vérifie toujours qu'un message\nest arrivé intact"," avant de lui faire confiance.",[593,1995,1997],{"id":1996},"dautres-types-de-trames","D'autres types de trames",[598,1999,2000],{},"Le NMEA 0183 définit des dizaines de trames. Les plus courantes :",[703,2002,2003,2013],{},[706,2004,2005],{},[709,2006,2007,2010],{},[712,2008,2009],{},"Type",[712,2011,2012],{},"Rôle",[722,2014,2015,2024,2034,2044,2054],{},[709,2016,2017,2021],{},[727,2018,2019],{},[626,2020,679],{},[727,2022,2023],{},"Position complète avec altitude",[709,2025,2026,2031],{},[727,2027,2028],{},[626,2029,2030],{},"$GPRMC",[727,2032,2033],{},"Position + vitesse + cap",[709,2035,2036,2041],{},[727,2037,2038],{},[626,2039,2040],{},"$GPGSA",[727,2042,2043],{},"Satellites utilisés et qualité géométrique",[709,2045,2046,2051],{},[727,2047,2048],{},[626,2049,2050],{},"$GPGSV",[727,2052,2053],{},"Satellites visibles dans le ciel",[709,2055,2056,2061],{},[727,2057,2058],{},[626,2059,2060],{},"$GPVTG",[727,2062,2063],{},"Vitesse et direction de déplacement",[598,2065,2066],{},"Un récepteur typique envoie plusieurs de ces trames par seconde. C'est à\nl'application qui les reçoit de choisir lesquelles décoder selon ses besoins.",[2068,2069,2070],"warning",{},[598,2071,2072,2073,2076],{},"Le format NMEA est ancien et présente plusieurs limites : précision réduite\n(quelques chiffres après la virgule), pas de chiffrement, débit faible (4800\nbauds par défaut). Les équipements modernes utilisent souvent ",[602,2074,2075],{},"NMEA 2000","\n(binaire, plus rapide) ou des protocoles propriétaires, mais NMEA 0183 reste\nla lingua franca pour l'apprentissage et les modules grand public.",[593,2078,2080],{"id":2079},"pour-aller-plus-loin","Pour aller plus loin",[598,2082,2083,2084,609],{},"La quasi-totalité des modules GPS « hobby » (par exemple le NEO-6M de\nu-blox, vendu une dizaine d'euros) sortent du NMEA 0183 sur leur port série.\nBranché à un Arduino ou à un Raspberry Pi, ce module permet de bricoler un\ntraceur de position en quelques lignes de code — un excellent projet pour\nprolonger ce cours dans le chapitre sur l'",[602,2085,2086],{},"informatique embarquée",[2088,2089,2090],"style",{},"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 .sIIMD, html code.shiki .sIIMD{--shiki-light:#032F62;--shiki-default:#032F62;--shiki-dark:#9ECBFF}html pre.shiki code .sBjJW, html code.shiki .sBjJW{--shiki-light:#005CC5;--shiki-default:#005CC5;--shiki-dark:#79B8FF}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":692,"searchDepth":1633,"depth":1633,"links":2092},[2093,2094,2095,2096,2097,2098,2099,2100],{"id":595,"depth":1633,"text":596},{"id":615,"depth":1633,"text":616},{"id":670,"depth":1633,"text":671},{"id":823,"depth":1633,"text":824},{"id":1579,"depth":1633,"text":1580},{"id":1967,"depth":1633,"text":1968},{"id":1996,"depth":1633,"text":1997},{"id":2079,"depth":1633,"text":2080},"La forme numérique brute d'une position GPS, et comment en extraire latitude et longitude.",null,"md",{},[2106,2110],{"slug":802,"kind":2107,"question":808,"choices":2108,"correct":800,"multi":2109,"explanation":801},"qcm",[815,737,820],false,{"slug":1946,"kind":2107,"question":1951,"choices":2111,"correct":800,"multi":2109,"explanation":1945},[1958,1961,1964],{"title":129,"description":2101},"bSF797YpFBP9VhLXQPuqacsCbebPk4GrffRCxMkzxxY",{"id":2115,"title":2116,"bo":2117,"body":2118,"description":2740,"eval":2102,"extension":2103,"labo":2102,"meta":2741,"navigation":2109,"path":2742,"quizzes":2743,"readingTime":1619,"seo":2744,"stem":2745,"tp":2102,"__hash__":2746},"coursMemo\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F2.trame-nmea.memo.md","Décoder une trame NMEA — l'essentiel",[588],{"type":590,"value":2119,"toc":2733},[2120,2124,2133,2137,2185,2464,2468,2517,2521,2558,2562,2663,2731],[593,2121,2123],{"id":2122},"en-une-phrase","En une phrase",[598,2125,2126,2127,2129,2130,2132],{},"Une trame ",[602,2128,608],{}," est une ligne de texte ASCII qui transporte une\nposition GPS sous forme de ",[602,2131,660],{},", lisible à\nl'œil nu.",[593,2134,2136],{"id":2135},"à-mémoriser","À mémoriser",[634,2138,2139,2145,2154,2162,2182],{},[637,2140,2141,2142],{},"Format : ",[626,2143,2144],{},"$GPxxx,champ1,champ2,...,*checksum",[637,2146,2147,2148,2150,2151,2153],{},"Commence toujours par ",[626,2149,653],{},", finit par ",[626,2152,1985],{}," + 2 caractères de vérification.",[637,2155,2156,2157,2161],{},"La trame la plus courante : ",[602,2158,2159],{},[626,2160,679],{}," (position + altitude).",[637,2163,2164,2165,2167,2168],{},"Coordonnées au format ",[602,2166,834],{},", pas en décimal :\n",[634,2169,2170,2176],{},[637,2171,2172,2173,2175],{},"latitude ",[626,2174,837],{}," (2 chiffres de degrés)",[637,2177,2178,2179,2181],{},"longitude ",[626,2180,841],{}," (3 chiffres de degrés)",[637,2183,2184],{},"Conversion en degrés décimaux :",[844,2186,2188],{"className":2187},[847],[844,2189,2191,2246],{"className":2190},[851],[844,2192,2194],{"className":2193},[855],[857,2195,2196],{"xmlns":859,"display":860},[862,2197,2198,2243],{},[865,2199,2200,2220,2222,2235,2237],{},[865,2201,2202,2204,2210,2212,2218],{},[870,2203,872],{},[874,2205,2206,2208],{"accent":876},[870,2207,879],{},[881,2209,883],{},[870,2211,886],{},[874,2213,2214,2216],{"accent":876},[870,2215,879],{},[881,2217,883],{},[870,2219,895],{},[881,2221,898],{},[865,2223,2224,2226,2232],{},[870,2225,872],{},[874,2227,2228,2230],{"accent":876},[870,2229,879],{},[881,2231,883],{},[870,2233,2234],{},"s",[881,2236,914],{},[916,2238,2239,2241],{},[870,2240,920],{},[922,2242,924],{},[926,2244,2245],{"encoding":928},"\\text{degrés décimaux} = \\text{degrés} + \\frac{\\text{minutes}}{60}",[844,2247,2249,2338,2393],{"className":2248,"ariaHidden":876},[933],[844,2250,2252,2255,2329,2332,2335],{"className":2251},[937],[844,2253],{"className":2254,"style":942},[941],[844,2256,2258,2261,2292,2295,2326],{"className":2257},[946,691],[844,2259,872],{"className":2260},[946],[844,2262,2264],{"className":2263},[946,953],[844,2265,2267],{"className":2266},[957],[844,2268,2270],{"className":2269},[961],[844,2271,2273,2281],{"className":2272,"style":966},[965],[844,2274,2275,2278],{"style":969},[844,2276],{"className":2277,"style":974},[973],[844,2279,879],{"className":2280},[946],[844,2282,2283,2286],{"style":969},[844,2284],{"className":2285,"style":974},[973],[844,2287,2289],{"className":2288,"style":987},[986],[844,2290,883],{"className":2291},[946],[844,2293,886],{"className":2294},[946],[844,2296,2298],{"className":2297},[946,953],[844,2299,2301],{"className":2300},[957],[844,2302,2304],{"className":2303},[961],[844,2305,2307,2315],{"className":2306,"style":966},[965],[844,2308,2309,2312],{"style":969},[844,2310],{"className":2311,"style":974},[973],[844,2313,879],{"className":2314},[946],[844,2316,2317,2320],{"style":969},[844,2318],{"className":2319,"style":974},[973],[844,2321,2323],{"className":2322,"style":987},[986],[844,2324,883],{"className":2325},[946],[844,2327,895],{"className":2328},[946],[844,2330],{"className":2331,"style":1032},[1031],[844,2333,898],{"className":2334},[1036],[844,2336],{"className":2337,"style":1032},[1031],[844,2339,2341,2344,2384,2387,2390],{"className":2340},[937],[844,2342],{"className":2343,"style":942},[941],[844,2345,2347,2350,2381],{"className":2346},[946,691],[844,2348,872],{"className":2349},[946],[844,2351,2353],{"className":2352},[946,953],[844,2354,2356],{"className":2355},[957],[844,2357,2359],{"className":2358},[961],[844,2360,2362,2370],{"className":2361,"style":966},[965],[844,2363,2364,2367],{"style":969},[844,2365],{"className":2366,"style":974},[973],[844,2368,879],{"className":2369},[946],[844,2371,2372,2375],{"style":969},[844,2373],{"className":2374,"style":974},[973],[844,2376,2378],{"className":2377,"style":987},[986],[844,2379,883],{"className":2380},[946],[844,2382,2234],{"className":2383},[946],[844,2385],{"className":2386,"style":1089},[1031],[844,2388,914],{"className":2389},[1093],[844,2391],{"className":2392,"style":1089},[1031],[844,2394,2396,2399],{"className":2395},[937],[844,2397],{"className":2398,"style":1103},[941],[844,2400,2402,2405,2461],{"className":2401},[946],[844,2403],{"className":2404},[1110,1111],[844,2406,2408],{"className":2407},[916],[844,2409,2411,2453],{"className":2410},[957,1118],[844,2412,2414,2450],{"className":2413},[961],[844,2415,2417,2428,2436],{"className":2416,"style":1125},[965],[844,2418,2419,2422],{"style":1128},[844,2420],{"className":2421,"style":974},[973],[844,2423,2425],{"className":2424},[946],[844,2426,924],{"className":2427},[946],[844,2429,2430,2433],{"style":1140},[844,2431],{"className":2432,"style":974},[973],[844,2434],{"className":2435,"style":1148},[1147],[844,2437,2438,2441],{"style":1151},[844,2439],{"className":2440,"style":974},[973],[844,2442,2444],{"className":2443},[946],[844,2445,2447],{"className":2446},[946,691],[844,2448,920],{"className":2449},[946],[844,2451,1168],{"className":2452},[1167],[844,2454,2456],{"className":2455},[961],[844,2457,2459],{"className":2458,"style":1175},[965],[844,2460],{},[844,2462],{"className":2463},[1181,1111],[593,2465,2467],{"id":2466},"à-savoir-reconnaître","À savoir reconnaître",[703,2469,2470,2480],{},[706,2471,2472],{},[709,2473,2474,2477],{},[712,2475,2476],{},"Trame",[712,2478,2479],{},"Information principale",[722,2481,2482,2491,2499,2508],{},[709,2483,2484,2488],{},[727,2485,2486],{},[626,2487,679],{},[727,2489,2490],{},"Position + altitude + heure",[709,2492,2493,2497],{},[727,2494,2495],{},[626,2496,2030],{},[727,2498,2033],{},[709,2500,2501,2505],{},[727,2502,2503],{},[626,2504,2050],{},[727,2506,2507],{},"Satellites visibles",[709,2509,2510,2514],{},[727,2511,2512],{},[626,2513,2060],{},[727,2515,2516],{},"Vitesse et direction",[593,2518,2520],{"id":2519},"pièges-courants","Pièges courants",[634,2522,2523,2536,2551],{},[637,2524,2525,2526],{},"Confondre minutes (NMEA) et fraction de degré (décimal).\n",[634,2527,2528],{},[637,2529,2530,2532,2533,609],{},[626,2531,747],{}," n'est pas 48,07° mais 48 + 7,038\u002F60 ≈ ",[602,2534,2535],{},"48,1173°",[637,2537,2538,2539,1786,2541,2544,2545,1786,2547,2550],{},"Oublier l'hémisphère (",[626,2540,760],{},[626,2542,2543],{},"S"," pour latitude, ",[626,2546,786],{},[626,2548,2549],{},"W"," pour longitude).",[637,2552,2553,2554,2557],{},"Penser que le ",[626,2555,2556],{},".0"," après les chiffres de degrés est décimal — c'est en fait\nle séparateur entre degrés et minutes.",[593,2559,2561],{"id":2560},"décoder-à-la-main-pseudo-code","Décoder à la main (pseudo-code)",[686,2563,2565],{"className":1611,"code":2564,"language":1613,"meta":692,"style":692},"trame = \"$GPGGA,123519,4807.038,N,01131.000,E,1,08,0.9,545.4,M,46.9,M,,*47\"\n\nchamps = decouper_autour_des_virgules(trame)\n\nheure       = champs[1]   # \"123519\"\nlatitude    = champs[2]   # \"4807.038\" → 48° + 7,038′\nhemisphere  = champs[3]   # \"N\"\nlongitude   = champs[4]   # \"01131.000\" → 011° + 31,000′\nmeridien    = champs[5]   # \"E\"\n",[626,2566,2567,2575,2579,2587,2591,2605,2620,2634,2649],{"__ignoreMap":692},[844,2568,2569,2571,2573],{"class":1618,"line":1619},[844,2570,1623],{"class":1622},[844,2572,898],{"class":1626},[844,2574,1630],{"class":1629},[844,2576,2577],{"class":1618,"line":1633},[844,2578,1637],{"emptyLinePlaceholder":1636},[844,2580,2581,2583,2585],{"class":1618,"line":1640},[844,2582,1643],{"class":1622},[844,2584,898],{"class":1626},[844,2586,1648],{"class":1622},[844,2588,2589],{"class":1618,"line":1651},[844,2590,1637],{"emptyLinePlaceholder":1636},[844,2592,2593,2595,2597,2599,2601,2603],{"class":1618,"line":1656},[844,2594,1659],{"class":1622},[844,2596,898],{"class":1626},[844,2598,1664],{"class":1622},[844,2600,800],{"class":1667},[844,2602,1670],{"class":1622},[844,2604,1674],{"class":1673},[844,2606,2607,2609,2611,2613,2615,2617],{"class":1618,"line":1677},[844,2608,1680],{"class":1622},[844,2610,898],{"class":1626},[844,2612,1664],{"class":1622},[844,2614,1687],{"class":1667},[844,2616,1670],{"class":1622},[844,2618,2619],{"class":1673},"# \"4807.038\" → 48° + 7,038′\n",[844,2621,2622,2624,2626,2628,2630,2632],{"class":1618,"line":1695},[844,2623,1698],{"class":1622},[844,2625,898],{"class":1626},[844,2627,1664],{"class":1622},[844,2629,1705],{"class":1667},[844,2631,1670],{"class":1622},[844,2633,1710],{"class":1673},[844,2635,2636,2638,2640,2642,2644,2646],{"class":1618,"line":1713},[844,2637,1716],{"class":1622},[844,2639,898],{"class":1626},[844,2641,1664],{"class":1622},[844,2643,1723],{"class":1667},[844,2645,1670],{"class":1622},[844,2647,2648],{"class":1673},"# \"01131.000\" → 011° + 31,000′\n",[844,2650,2651,2653,2655,2657,2659,2661],{"class":1618,"line":1731},[844,2652,1734],{"class":1622},[844,2654,898],{"class":1626},[844,2656,1664],{"class":1622},[844,2658,1741],{"class":1667},[844,2660,1670],{"class":1622},[844,2662,1746],{"class":1673},[598,2664,2665,2666,2669,2670,2673,2674,609],{},"Pour la conversion en degrés décimaux : on prend les ",[602,2667,2668],{},"deux premiers\ncaractères"," pour les degrés, ",[602,2671,2672],{},"le reste"," pour les minutes, et on applique\n",[844,2675,2677,2698],{"className":2676},[851],[844,2678,2680],{"className":2679},[855],[857,2681,2682],{"xmlns":859},[862,2683,2684,2696],{},[865,2685,2686,2688,2690,2692,2694],{},[1238,2687,1778],{},[881,2689,914],{},[1238,2691,1783],{},[1238,2693,1786],{"mathvariant":1240},[922,2695,924],{},[926,2697,1791],{"encoding":928},[844,2699,2701,2719],{"className":2700,"ariaHidden":876},[933],[844,2702,2704,2707,2710,2713,2716],{"className":2703},[937],[844,2705],{"className":2706,"style":1801},[941],[844,2708,1778],{"className":2709,"style":1806},[946,1805],[844,2711],{"className":2712,"style":1089},[1031],[844,2714,914],{"className":2715},[1093],[844,2717],{"className":2718,"style":1089},[1031],[844,2720,2722,2725,2728],{"className":2721},[937],[844,2723],{"className":2724,"style":1822},[941],[844,2726,1783],{"className":2727,"style":1826},[946,1805],[844,2729,1830],{"className":2730},[946],[2088,2732,2090],{},{"title":692,"searchDepth":1633,"depth":1633,"links":2734},[2735,2736,2737,2738,2739],{"id":2122,"depth":1633,"text":2123},{"id":2135,"depth":1633,"text":2136},{"id":2466,"depth":1633,"text":2467},{"id":2519,"depth":1633,"text":2520},{"id":2560,"depth":1633,"text":2561},"Mémo de révision sur le protocole NMEA 0183.",{},"\u002Fsnt-2nde\u002Fse-localisation-cartographie\u002Ftrame-nmea.memo",[],{"title":2116,"description":2740},"0.snt-2nde\u002Fse-localisation-cartographie\u002F2.trame-nmea.memo","yFyJki2MFsV3M7JL7o2hW62vC4GkuLQpYQwZ5FN0wmc",{"id":2748,"title":2749,"body":2750,"description":3571,"extension":2103,"meta":3572,"navigation":2109,"path":3573,"seo":3574,"stem":3575,"__hash__":3576},"coursSlides\u002F0.snt-2nde\u002Fse-localisation-cartographie\u002F2.trame-nmea.slides.md","Décoder une trame NMEA — diapositives",{"type":590,"value":2751,"toc":3569},[2752,2756,2759,2762,2766,2791,2793,2797,2802,2810,2812,2816,2874,2877,2879,2883,2891,2894,3132,3333,3339,3341,3345,3445,3505,3507,3511,3517,3524,3526,3530,3547,3554,3556,3560,3567],[2753,2754,129],"h1",{"id":2755},"décoder-une-trame-nmea",[598,2757,2758],{},"Comment une position GPS arrive-t-elle jusqu'à votre application ?",[2760,2761],"hr",{},[2753,2763,2765],{"id":2764},"nmea-0183-lessentiel","NMEA 0183 — l'essentiel",[634,2767,2768,2774,2781,2784],{},[637,2769,2770,2771,2773],{},"Protocole ",[602,2772,642],{}," (ASCII lisible)",[637,2775,2776,2777,2780],{},"Né en ",[602,2778,2779],{},"1983",", standard maritime",[637,2782,2783],{},"Devenu universel pour les modules GPS grand public",[637,2785,2786,2787,2790],{},"Champs séparés par des ",[602,2788,2789],{},"virgules"," (comme un CSV)",[2760,2792],{},[2753,2794,2796],{"id":2795},"une-trame-exemple","Une trame exemple",[686,2798,2800],{"className":2799,"code":690,"language":691,"meta":692},[689],[626,2801,690],{"__ignoreMap":692},[598,2803,2804,2805,2807,2808,609],{},"Une ligne de texte, des champs séparés par des virgules,\nterminée par un ",[602,2806,1978],{}," ",[626,2809,1974],{},[2760,2811],{},[2753,2813,2815],{"id":2814},"les-champs-principaux-à-reconnaître","Les champs principaux à reconnaître",[703,2817,2818,2827],{},[706,2819,2820],{},[709,2821,2822,2824],{},[712,2823,714],{},[712,2825,2826],{},"Sens",[722,2828,2829,2838,2847,2856,2865],{},[709,2830,2831,2835],{},[727,2832,2833],{},[626,2834,734],{},[727,2836,2837],{},"heure UTC : 12h 35min 19s",[709,2839,2840,2844],{},[727,2841,2842],{},[626,2843,747],{},[727,2845,2846],{},"latitude : 48° 07,038′",[709,2848,2849,2853],{},[727,2850,2851],{},[626,2852,760],{},[727,2854,2855],{},"hémisphère Nord",[709,2857,2858,2862],{},[727,2859,2860],{},[626,2861,773],{},[727,2863,2864],{},"longitude : 011° 31,000′",[709,2866,2867,2871],{},[727,2868,2869],{},[626,2870,786],{},[727,2872,2873],{},"méridien Est",[598,2875,2876],{},"Le reste (qualité, nombre de satellites, altitude…) n'est pas exigible.",[2760,2878],{},[2753,2880,2882],{"id":2881},"degrés-minutes-vs-degrés-décimaux","Degrés-minutes vs degrés décimaux",[598,2884,2885,2886,2890],{},"NMEA → ",[602,2887,2888],{},[626,2889,837],{}," (degrés + minutes)",[598,2892,2893],{},"Conversion :",[844,2895,2897],{"className":2896},[847],[844,2898,2900,2948],{"className":2899},[851],[844,2901,2903],{"className":2902},[855],[857,2904,2905],{"xmlns":859,"display":860},[862,2906,2907,2945],{},[865,2908,2909,2923,2925,2937,2939],{},[865,2910,2911,2914,2920],{},[870,2912,2913],{},"d",[874,2915,2916,2918],{"accent":876},[870,2917,879],{},[881,2919,883],{},[870,2921,2922],{},"cimal",[881,2924,898],{},[865,2926,2927,2929,2935],{},[870,2928,872],{},[874,2930,2931,2933],{"accent":876},[870,2932,879],{},[881,2934,883],{},[870,2936,2234],{},[881,2938,914],{},[916,2940,2941,2943],{},[870,2942,920],{},[922,2944,924],{},[926,2946,2947],{"encoding":928},"\\text{décimal} = \\text{degrés} + \\frac{\\text{minutes}}{60}",[844,2949,2951,3006,3061],{"className":2950,"ariaHidden":876},[933],[844,2952,2954,2957,2997,3000,3003],{"className":2953},[937],[844,2955],{"className":2956,"style":966},[941],[844,2958,2960,2963,2994],{"className":2959},[946,691],[844,2961,2913],{"className":2962},[946],[844,2964,2966],{"className":2965},[946,953],[844,2967,2969],{"className":2968},[957],[844,2970,2972],{"className":2971},[961],[844,2973,2975,2983],{"className":2974,"style":966},[965],[844,2976,2977,2980],{"style":969},[844,2978],{"className":2979,"style":974},[973],[844,2981,879],{"className":2982},[946],[844,2984,2985,2988],{"style":969},[844,2986],{"className":2987,"style":974},[973],[844,2989,2991],{"className":2990,"style":987},[986],[844,2992,883],{"className":2993},[946],[844,2995,2922],{"className":2996},[946],[844,2998],{"className":2999,"style":1032},[1031],[844,3001,898],{"className":3002},[1036],[844,3004],{"className":3005,"style":1032},[1031],[844,3007,3009,3012,3052,3055,3058],{"className":3008},[937],[844,3010],{"className":3011,"style":942},[941],[844,3013,3015,3018,3049],{"className":3014},[946,691],[844,3016,872],{"className":3017},[946],[844,3019,3021],{"className":3020},[946,953],[844,3022,3024],{"className":3023},[957],[844,3025,3027],{"className":3026},[961],[844,3028,3030,3038],{"className":3029,"style":966},[965],[844,3031,3032,3035],{"style":969},[844,3033],{"className":3034,"style":974},[973],[844,3036,879],{"className":3037},[946],[844,3039,3040,3043],{"style":969},[844,3041],{"className":3042,"style":974},[973],[844,3044,3046],{"className":3045,"style":987},[986],[844,3047,883],{"className":3048},[946],[844,3050,2234],{"className":3051},[946],[844,3053],{"className":3054,"style":1089},[1031],[844,3056,914],{"className":3057},[1093],[844,3059],{"className":3060,"style":1089},[1031],[844,3062,3064,3067],{"className":3063},[937],[844,3065],{"className":3066,"style":1103},[941],[844,3068,3070,3073,3129],{"className":3069},[946],[844,3071],{"className":3072},[1110,1111],[844,3074,3076],{"className":3075},[916],[844,3077,3079,3121],{"className":3078},[957,1118],[844,3080,3082,3118],{"className":3081},[961],[844,3083,3085,3096,3104],{"className":3084,"style":1125},[965],[844,3086,3087,3090],{"style":1128},[844,3088],{"className":3089,"style":974},[973],[844,3091,3093],{"className":3092},[946],[844,3094,924],{"className":3095},[946],[844,3097,3098,3101],{"style":1140},[844,3099],{"className":3100,"style":974},[973],[844,3102],{"className":3103,"style":1148},[1147],[844,3105,3106,3109],{"style":1151},[844,3107],{"className":3108,"style":974},[973],[844,3110,3112],{"className":3111},[946],[844,3113,3115],{"className":3114},[946,691],[844,3116,920],{"className":3117},[946],[844,3119,1168],{"className":3120},[1167],[844,3122,3124],{"className":3123},[961],[844,3125,3127],{"className":3126,"style":1175},[965],[844,3128],{},[844,3130],{"className":3131},[1181,1111],[598,3133,3134,3136,3137,3233,3136,3235],{},[626,3135,747],{}," ⇒ ",[844,3138,3140,3167],{"className":3139},[851],[844,3141,3143],{"className":3142},[855],[857,3144,3145],{"xmlns":859},[862,3146,3147,3165],{},[865,3148,3149,3151,3153,3155,3157,3159,3161,3163],{},[922,3150,1195],{},[881,3152,914],{},[922,3154,1229],{},[1238,3156,1786],{"mathvariant":1240},[922,3158,924],{},[881,3160,898],{},[922,3162,1236],{},[1238,3164,1241],{"mathvariant":1240},[926,3166,1874],{"encoding":928},[844,3168,3170,3188,3215],{"className":3169,"ariaHidden":876},[933],[844,3171,3173,3176,3179,3182,3185],{"className":3172},[937],[844,3174],{"className":3175,"style":1254},[941],[844,3177,1195],{"className":3178},[946],[844,3180],{"className":3181,"style":1089},[1031],[844,3183,914],{"className":3184},[1093],[844,3186],{"className":3187,"style":1089},[1031],[844,3189,3191,3194,3197,3203,3206,3209,3212],{"className":3190},[937],[844,3192],{"className":3193,"style":1822},[941],[844,3195,1323],{"className":3196},[946],[844,3198,3200],{"className":3199},[946],[844,3201,1331],{"className":3202},[1330],[844,3204,1914],{"className":3205},[946],[844,3207],{"className":3208,"style":1032},[1031],[844,3210,898],{"className":3211},[1036],[844,3213],{"className":3214,"style":1032},[1031],[844,3216,3218,3221,3224,3230],{"className":3217},[937],[844,3219],{"className":3220,"style":942},[941],[844,3222,1195],{"className":3223},[946],[844,3225,3227],{"className":3226},[946],[844,3228,1331],{"className":3229},[1330],[844,3231,1377],{"className":3232},[946],[626,3234,773],{},[844,3236,3238,3266],{"className":3237},[851],[844,3239,3241],{"className":3240},[855],[857,3242,3243],{"xmlns":859},[862,3244,3245,3263],{},[865,3246,3247,3249,3251,3253,3255,3257,3259,3261],{},[922,3248,1411],{},[881,3250,914],{},[922,3252,1394],{},[1238,3254,1786],{"mathvariant":1240},[922,3256,924],{},[881,3258,898],{},[922,3260,1426],{},[1238,3262,1241],{"mathvariant":1240},[926,3264,3265],{"encoding":928},"11 + 31{,}000\u002F60 = 11{,}5167°",[844,3267,3269,3287,3315],{"className":3268,"ariaHidden":876},[933],[844,3270,3272,3275,3278,3281,3284],{"className":3271},[937],[844,3273],{"className":3274,"style":1254},[941],[844,3276,1411],{"className":3277},[946],[844,3279],{"className":3280,"style":1089},[1031],[844,3282,914],{"className":3283},[1093],[844,3285],{"className":3286,"style":1089},[1031],[844,3288,3290,3293,3296,3302,3306,3309,3312],{"className":3289},[937],[844,3291],{"className":3292,"style":1822},[941],[844,3294,1507],{"className":3295},[946],[844,3297,3299],{"className":3298},[946],[844,3300,1331],{"className":3301},[1330],[844,3303,3305],{"className":3304},[946],"000\u002F60",[844,3307],{"className":3308,"style":1032},[1031],[844,3310,898],{"className":3311},[1036],[844,3313],{"className":3314,"style":1032},[1031],[844,3316,3318,3321,3324,3330],{"className":3317},[937],[844,3319],{"className":3320,"style":942},[941],[844,3322,1411],{"className":3323},[946],[844,3325,3327],{"className":3326},[946],[844,3328,1331],{"className":3329},[1330],[844,3331,1559],{"className":3332},[946],[598,3334,3335,3336,609],{},"⇒ ",[602,3337,3338],{},"Munich",[2760,3340],{},[2753,3342,3344],{"id":3343},"décoder-à-la-main","Décoder à la main",[686,3346,3348],{"className":1611,"code":3347,"language":1613,"meta":692,"style":692},"trame = \"$GPGGA,123519,4807.038,N,01131.000,E,...\"\n\nchamps = decouper_autour_des_virgules(trame)\n\nheure       = champs[1]   # \"123519\"\nlatitude    = champs[2]   # \"4807.038\"\nhemisphere  = champs[3]   # \"N\"\nlongitude   = champs[4]   # \"01131.000\"\nmeridien    = champs[5]   # \"E\"\n",[626,3349,3350,3359,3363,3371,3375,3389,3403,3417,3431],{"__ignoreMap":692},[844,3351,3352,3354,3356],{"class":1618,"line":1619},[844,3353,1623],{"class":1622},[844,3355,898],{"class":1626},[844,3357,3358],{"class":1629}," \"$GPGGA,123519,4807.038,N,01131.000,E,...\"\n",[844,3360,3361],{"class":1618,"line":1633},[844,3362,1637],{"emptyLinePlaceholder":1636},[844,3364,3365,3367,3369],{"class":1618,"line":1640},[844,3366,1643],{"class":1622},[844,3368,898],{"class":1626},[844,3370,1648],{"class":1622},[844,3372,3373],{"class":1618,"line":1651},[844,3374,1637],{"emptyLinePlaceholder":1636},[844,3376,3377,3379,3381,3383,3385,3387],{"class":1618,"line":1656},[844,3378,1659],{"class":1622},[844,3380,898],{"class":1626},[844,3382,1664],{"class":1622},[844,3384,800],{"class":1667},[844,3386,1670],{"class":1622},[844,3388,1674],{"class":1673},[844,3390,3391,3393,3395,3397,3399,3401],{"class":1618,"line":1677},[844,3392,1680],{"class":1622},[844,3394,898],{"class":1626},[844,3396,1664],{"class":1622},[844,3398,1687],{"class":1667},[844,3400,1670],{"class":1622},[844,3402,1692],{"class":1673},[844,3404,3405,3407,3409,3411,3413,3415],{"class":1618,"line":1695},[844,3406,1698],{"class":1622},[844,3408,898],{"class":1626},[844,3410,1664],{"class":1622},[844,3412,1705],{"class":1667},[844,3414,1670],{"class":1622},[844,3416,1710],{"class":1673},[844,3418,3419,3421,3423,3425,3427,3429],{"class":1618,"line":1713},[844,3420,1716],{"class":1622},[844,3422,898],{"class":1626},[844,3424,1664],{"class":1622},[844,3426,1723],{"class":1667},[844,3428,1670],{"class":1622},[844,3430,1728],{"class":1673},[844,3432,3433,3435,3437,3439,3441,3443],{"class":1618,"line":1731},[844,3434,1734],{"class":1622},[844,3436,898],{"class":1626},[844,3438,1664],{"class":1622},[844,3440,1741],{"class":1667},[844,3442,1670],{"class":1622},[844,3444,1746],{"class":1673},[598,3446,3447,3448,609],{},"Pseudo-code : on découpe, on lit chaque champ.\nConversion degrés-minutes → décimaux : ",[844,3449,3451,3472],{"className":3450},[851],[844,3452,3454],{"className":3453},[855],[857,3455,3456],{"xmlns":859},[862,3457,3458,3470],{},[865,3459,3460,3462,3464,3466,3468],{},[1238,3461,1778],{},[881,3463,914],{},[1238,3465,1783],{},[1238,3467,1786],{"mathvariant":1240},[922,3469,924],{},[926,3471,1791],{"encoding":928},[844,3473,3475,3493],{"className":3474,"ariaHidden":876},[933],[844,3476,3478,3481,3484,3487,3490],{"className":3477},[937],[844,3479],{"className":3480,"style":1801},[941],[844,3482,1778],{"className":3483,"style":1806},[946,1805],[844,3485],{"className":3486,"style":1089},[1031],[844,3488,914],{"className":3489},[1093],[844,3491],{"className":3492,"style":1089},[1031],[844,3494,3496,3499,3502],{"className":3495},[937],[844,3497],{"className":3498,"style":1822},[941],[844,3500,1783],{"className":3501,"style":1826},[946,1805],[844,3503,1830],{"className":3504},[946],[2760,3506],{},[2753,3508,3510],{"id":3509},"le-checksum","Le checksum",[598,3512,3513,3514,3516],{},"Le ",[626,3515,1974],{}," final = vérification d'intégrité (XOR des caractères, en hexa).",[598,3518,3519,3520,3523],{},"Principe général : ",[602,3521,3522],{},"on vérifie toujours qu'un message est arrivé intact","\navant d'y faire confiance.",[2760,3525],{},[2753,3527,3529],{"id":3528},"autres-trames-courantes","Autres trames courantes",[634,3531,3532,3537,3542],{},[637,3533,3534,3536],{},[626,3535,2030],{}," — position + vitesse + cap",[637,3538,3539,3541],{},[626,3540,2050],{}," — satellites visibles",[637,3543,3544,3546],{},[626,3545,2060],{}," — vitesse et direction",[598,3548,3549,3550,3553],{},"Plusieurs trames émises ",[602,3551,3552],{},"par seconde"," : l'application choisit ce qu'elle\ndécode.",[2760,3555],{},[2753,3557,3559],{"id":3558},"à-retenir","À retenir",[598,3561,3562,3563,3566],{},"Une trame NMEA est ",[602,3564,3565],{},"un message texte simple, vieux et durable",".\nSavoir le décoder, c'est savoir lire à la source ce qu'un 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