{"id":1911,"date":"2025-07-03T19:23:14","date_gmt":"2025-07-03T18:23:14","guid":{"rendered":"https:\/\/workboot.fr\/ciela\/?page_id=1911"},"modified":"2025-07-12T15:55:22","modified_gmt":"2025-07-12T14:55:22","slug":"les-bases-en-mathematique","status":"publish","type":"page","link":"https:\/\/workboot.fr\/ciela\/les-bases-en-mathematique\/","title":{"rendered":"Les bases en math\u00e9matique"},"content":{"rendered":"\n<nav aria-label=\"Table des mati\u00e8res\" class=\"wp-block-table-of-contents\"><ol><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/workboot.fr\/ciela\/les-bases-en-mathematique\/#synthese-des-bases-de-numeration-courantes-en-informatique\">Synth\u00e8se des bases de num\u00e9ration courantes en informatique<\/a><ol><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/workboot.fr\/ciela\/les-bases-en-mathematique\/#1-base-2-binaire\">1. Base 2 \u2014 Binaire<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/workboot.fr\/ciela\/les-bases-en-mathematique\/#2-base-8-octale\">2. Base 8 \u2014 Octale<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/workboot.fr\/ciela\/les-bases-en-mathematique\/#3-base-10-decimale\">3. Base 10 \u2014 D\u00e9cimale<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/workboot.fr\/ciela\/les-bases-en-mathematique\/#4-base-16-hexadecimale\">4. Base 16 \u2014 Hexad\u00e9cimale<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/workboot.fr\/ciela\/les-bases-en-mathematique\/#pourquoi-ces-bases-en-informatique\">Pourquoi ces bases en informatique ?<\/a><\/li><\/ol><\/li><\/ol><\/nav>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"synthese-des-bases-de-numeration-courantes-en-informatique\">Synth\u00e8se des bases de num\u00e9ration courantes en informatique<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"1-base-2-binaire\">1. <strong>Base 2 \u2014 Binaire<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Chiffres utilis\u00e9s<\/strong> : 0, 1<\/li>\n\n\n\n<li><strong>Utilisation<\/strong> : Repr\u00e9sentation fondamentale des donn\u00e9es en informatique (bits).<\/li>\n\n\n\n<li><strong>Exemple<\/strong> :\n<ul class=\"wp-block-list\">\n<li>10112=1\u00d723+0\u00d722+1\u00d721+1\u00d720=11101011_2 = 1 \\times 2^3 + 0 \\times 2^2 + 1 \\times 2^1 + 1 \\times 2^0 = 11_{10}10112\u200b=1\u00d723+0\u00d722+1\u00d721+1\u00d720=1110\u200b<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"2-base-8-octale\">2. <strong>Base 8 \u2014 Octale<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Chiffres utilis\u00e9s<\/strong> : 0 \u00e0 7<\/li>\n\n\n\n<li><strong>Utilisation<\/strong> : Historique, simplifie la lecture des donn\u00e9es binaires (chaque chiffre octal correspond \u00e0 3 bits).<\/li>\n\n\n\n<li><strong>Exemple<\/strong> :\n<ul class=\"wp-block-list\">\n<li>178=1\u00d781+7\u00d780=151017_8 = 1 \\times 8^1 + 7 \\times 8^0 = 15_{10}178\u200b=1\u00d781+7\u00d780=1510\u200b<\/li>\n\n\n\n<li>En binaire : 178=001111217_8 = 001 111_2178\u200b=0011112\u200b<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"3-base-10-decimale\">3. <strong>Base 10 \u2014 D\u00e9cimale<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Chiffres utilis\u00e9s<\/strong> : 0 \u00e0 9<\/li>\n\n\n\n<li><strong>Utilisation<\/strong> : Syst\u00e8me usuel pour les humains, base naturelle.<\/li>\n\n\n\n<li><strong>Exemple<\/strong> :\n<ul class=\"wp-block-list\">\n<li>34510=3\u00d7102+4\u00d7101+5\u00d7100345_{10} = 3 \\times 10^2 + 4 \\times 10^1 + 5 \\times 10^034510\u200b=3\u00d7102+4\u00d7101+5\u00d7100<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"4-base-16-hexadecimale\">4. <strong>Base 16 \u2014 Hexad\u00e9cimale<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Chiffres utilis\u00e9s<\/strong> : 0 \u00e0 9, puis A (10) \u00e0 F (15)<\/li>\n\n\n\n<li><strong>Utilisation<\/strong> : Tr\u00e8s utilis\u00e9e en informatique pour repr\u00e9senter les donn\u00e9es de fa\u00e7on compacte (chaque chiffre hexad\u00e9cimal correspond \u00e0 4 bits).<\/li>\n\n\n\n<li><strong>Exemple<\/strong> :\n<ul class=\"wp-block-list\">\n<li>1F16=1\u00d7161+15\u00d7160=31101F_{16} = 1 \\times 16^1 + 15 \\times 16^0 = 31_{10}1F16\u200b=1\u00d7161+15\u00d7160=3110\u200b<\/li>\n\n\n\n<li>En binaire : 1F16=0001111121F_{16} = 0001 1111_21F16\u200b=000111112\u200b<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"pourquoi-ces-bases-en-informatique\">Pourquoi ces bases en informatique ?<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Le <strong>binaire<\/strong> est la base \u00ab native \u00bb des ordinateurs (transistors on\/off).<\/li>\n\n\n\n<li>L\u2019<strong>octal<\/strong> et l\u2019<strong>hexad\u00e9cimal<\/strong> simplifient la lecture et l\u2019\u00e9criture des longues cha\u00eenes binaires.<\/li>\n\n\n\n<li>Le <strong>d\u00e9cimal<\/strong> reste la base naturelle pour les humains.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Synth\u00e8se des bases de num\u00e9ration courantes en informatique 1. Base 2 \u2014 Binaire 2. Base 8 \u2014 Octale 3. Base 10 \u2014 D\u00e9cimale 4. Base 16 \u2014 Hexad\u00e9cimale Pourquoi ces bases en informatique ?<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_uag_custom_page_level_css":"","footnotes":""},"class_list":["post-1911","page","type-page","status-publish","hentry"],"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false},"uagb_author_info":{"display_name":"admin","author_link":"https:\/\/workboot.fr\/ciela\/author\/admin\/"},"uagb_comment_info":0,"uagb_excerpt":"Synth\u00e8se des bases de num\u00e9ration courantes en informatique 1. Base 2 \u2014 Binaire 2. Base 8 \u2014 Octale 3. Base 10 \u2014 D\u00e9cimale 4. Base 16 \u2014 Hexad\u00e9cimale Pourquoi ces bases en informatique ?","_links":{"self":[{"href":"https:\/\/workboot.fr\/ciela\/wp-json\/wp\/v2\/pages\/1911","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workboot.fr\/ciela\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/workboot.fr\/ciela\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/workboot.fr\/ciela\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workboot.fr\/ciela\/wp-json\/wp\/v2\/comments?post=1911"}],"version-history":[{"count":2,"href":"https:\/\/workboot.fr\/ciela\/wp-json\/wp\/v2\/pages\/1911\/revisions"}],"predecessor-version":[{"id":2320,"href":"https:\/\/workboot.fr\/ciela\/wp-json\/wp\/v2\/pages\/1911\/revisions\/2320"}],"wp:attachment":[{"href":"https:\/\/workboot.fr\/ciela\/wp-json\/wp\/v2\/media?parent=1911"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}