{"id":10532,"date":"2022-11-20T00:58:11","date_gmt":"2022-11-19T23:58:11","guid":{"rendered":"https:\/\/www.auditsi.eu\/?p=10532"},"modified":"2022-11-20T01:08:34","modified_gmt":"2022-11-20T00:08:34","slug":"algebre-de-boole-ou-arithmetique-booleenne","status":"publish","type":"post","link":"https:\/\/www.auditsi.eu\/?p=10532","title":{"rendered":"Alg\u00e8bre de Boole (ou arithm\u00e9tique bool\u00e9enne)"},"content":{"rendered":"<p style=\"text-align: justify;\">L&#8217;arithm\u00e9tique bool\u00e9enne est une <strong>approche alg\u00e9brique de la logique<\/strong> utilis\u00e9e commun\u00e9ment en informatique avec certaines fonctions d\u2019Excel ainsi qu\u2019en programmation (exemple VBA) et requ\u00eates SQL dans un <strong>processus d\u2019ex\u00e9cution conditionnelle<\/strong>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-10533\" src=\"https:\/\/www.auditsi.eu\/wp-content\/uploads\/2022\/11\/OPERATEURS-DE-COMPARAISON.png\" alt=\"OPERATEURS DE COMPARAISON\" width=\"745\" height=\"266\" srcset=\"https:\/\/www.auditsi.eu\/wp-content\/uploads\/2022\/11\/OPERATEURS-DE-COMPARAISON.png 745w, https:\/\/www.auditsi.eu\/wp-content\/uploads\/2022\/11\/OPERATEURS-DE-COMPARAISON-300x107.png 300w, https:\/\/www.auditsi.eu\/wp-content\/uploads\/2022\/11\/OPERATEURS-DE-COMPARAISON-730x261.png 730w\" sizes=\"auto, (max-width: 745px) 100vw, 745px\" \/><\/p>\n<p style=\"text-align: justify;\">L&#8217;alg\u00e8bre de Boole repose sur l&#8217;<strong>expression de comparaisons<\/strong> renvoyant <strong>VRAI<\/strong> (TRUE) ou <strong>FAUX<\/strong> (FALSE) soit respectivement <strong>1 et 0<\/strong> suivant que la comparaison est correcte ou non.<\/p>\n<p style=\"text-align: justify;\">L\u2019expression de comparaisons est utilis\u00e9e pour <strong>d\u00e9finir des crit\u00e8res<\/strong> (tests conditionnels) <strong>conditionnant la r\u00e9alisation d\u2019actions ou de calculs<\/strong>.<\/p>\n<p style=\"text-align: justify;\">Structures de tests conditionnels :<\/p>\n<ul>\n<li style=\"text-align: justify;\">EXCEL : SI(\u2026;\u2026;\u2026) ; SI.CONDITIONS\u2026<\/li>\n<li style=\"text-align: justify;\">VBA \/ BASIC : <a href=\"https:\/\/www.auditsi.eu\/?p=1797\">IF\u2026 THEN\u2026 ELSEIF\u2026 ELSE\u2026<\/a><\/li>\n<li style=\"text-align: justify;\">SQL : <a href=\"https:\/\/www.auditsi.eu\/?p=8216\">IIf(\u2026,\u2026,\u2026)<\/a><\/li>\n<\/ul>\n<p>La comparaison <strong>associe deux valeurs<\/strong> (ou bien variables) <strong>et un <a href=\"https:\/\/www.auditsi.eu\/?p=6979\">op\u00e9rateur de comparaison<\/a><\/strong> (&lt;, &gt;=, =, &gt;=, &gt; ou &lt;&gt;).<\/p>\n<p style=\"text-align: justify;\">Exemple : 1 &gt; 5 renvoie FAUX ou 0<\/p>\n<p style=\"text-align: justify;\">Les <strong>comparaisons multiples<\/strong> (multicrit\u00e8res) sont li\u00e9es par des <a href=\"https:\/\/www.auditsi.eu\/?p=6975\"><strong>op\u00e9rateurs logiques<\/strong><\/a> (ou bool\u00e9ens). Dans la plupart des langages informatiques, les op\u00e9rateurs logiques sont g\u00e9n\u00e9ralement OR (ou), AND (et) ou XOR (ou exclusif).<\/p>\n<p style=\"text-align: justify;\">EXCEL utilise les fonctions ET() et OU () par exemple avec la fonction SI() ainsi que les signes * et + pour exprimer respectivement les op\u00e9rateurs ET et OU avec les <a href=\"https:\/\/www.auditsi.eu\/?p=10382\">fonctions RECHERCHEX<\/a> et FILTRE.<\/p>\n<p style=\"text-align: justify;\">Par exemple (1&gt;5)*(2&lt;5) \u00e9quivaut \u00e0 0 (FAUX) * 1 (VRAI) = 0 : la condition n\u2019est pas r\u00e9alis\u00e9e<\/p>\n<p style=\"text-align: justify;\">Par exemple (1&gt;5)+(2&lt;5) \u00e9quivaut \u00e0 0 (FAUX) + 1 (VRAI) = 1 : la condition est r\u00e9alis\u00e9e<\/p>\n<p style=\"text-align: justify;\">Il est bien entendu possible d\u2019associer les diff\u00e9rents op\u00e9rateurs logiques dans la m\u00eame comparaisons et m\u00eame d\u2019utiliser les parenth\u00e8ses pour exprimer des comparaisons plus complexes.<\/p>\n<p style=\"text-align: justify;\">Exemple : (1&gt;5)*((6&gt;3)+(10&lt;=20)) \u00e9quivaut \u00e0 0 * (1+0) = 0<\/p>\n<p>___<\/p>\n<p>Approfondir le sujet :&nbsp;<a href=\"https:\/\/www.auditsi.eu\/?cat=2765\">Analyse de donn\u00e9es et automatisation<\/a>&nbsp;\/&nbsp;<a href=\"https:\/\/www.auditsi.eu\/?glossary=excel\">Tout savoir sur Excel<\/a>&nbsp;\/&nbsp;<a title=\"S\u00e9rie d'articles Ma\u00eetriser Excel\" href=\"https:\/\/www.auditsi.eu\/?p=4475\">D\u00e9couvrir la s\u00e9rie d\u2019articles Ma\u00eetriser Excel<\/a><\/p>\n<div id=\"sconnect-is-installed\" style=\"display: none;\">2.13.0.0<\/div>\n<div id=\"sconnect-is-installed\" style=\"display: none;\">2.13.0.0<\/div>\n<div id=\"sconnect-is-installed\" style=\"display: none;\">2.13.0.0<\/div>\n<div style=\"padding-bottom:20px; padding-top:10px;\" class=\"hupso-share-buttons\"><!-- Hupso Share Buttons - https:\/\/www.hupso.com\/share\/ --><a class=\"hupso_counters\" href=\"https:\/\/www.hupso.com\/share\/\"><img decoding=\"async\" src=\"https:\/\/static.hupso.com\/share\/buttons\/lang\/fr\/share-small.png\" style=\"border:0px; padding-top:2px; float:left;\" alt=\"Share Button\"\/><\/a><script type=\"text\/javascript\">var hupso_services_c=new Array(\"twitter\",\"facebook_like\",\"facebook_send\",\"email\",\"print\",\"linkedin\");var hupso_counters_lang = \"fr_FR\";var hupso_image_folder_url = \"\";var hupso_twitter_via=\"BenoitRiviere14\";var hupso_url_c=\"\";var hupso_title_c=\"Alg%C3%A8bre%20de%20Boole%20%28ou%20arithm%C3%A9tique%20bool%C3%A9enne%29\";<\/script><script type=\"text\/javascript\" src=\"https:\/\/static.hupso.com\/share\/js\/counters.js\"><\/script><!-- Hupso Share Buttons --><\/div>","protected":false},"excerpt":{"rendered":"<p>L&#8217;arithm\u00e9tique bool\u00e9enne est une approche alg\u00e9brique de la logique utilis\u00e9e commun\u00e9ment en informatique avec certaines fonctions d\u2019Excel ainsi qu\u2019en programmation (exemple VBA) et requ\u00eates SQL dans un processus d\u2019ex\u00e9cution conditionnelle. L&#8217;alg\u00e8bre de Boole repose sur l&#8217;expression de comparaisons renvoyant VRAI (TRUE) ou FAUX (FALSE) soit respectivement 1 et 0 suivant que la comparaison est correcte &#8230;<\/p>\n<p><a href=\"https:\/\/www.auditsi.eu\/?p=10532\" class=\"more-link\">Continue reading &lsquo;Alg\u00e8bre de Boole (ou arithm\u00e9tique bool\u00e9enne)&rsquo; &raquo;<\/a><\/p>\n<div style=\"padding-bottom:20px; padding-top:10px;\" class=\"hupso-share-buttons\"><!-- Hupso Share Buttons - https:\/\/www.hupso.com\/share\/ --><a class=\"hupso_counters\" href=\"https:\/\/www.hupso.com\/share\/\"><img src=\"https:\/\/static.hupso.com\/share\/buttons\/lang\/fr\/share-small.png\" style=\"border:0px; padding-top:2px; float:left;\" alt=\"Share Button\"\/><\/a><script type=\"text\/javascript\">var hupso_services_c=new Array(\"twitter\",\"facebook_like\",\"facebook_send\",\"email\",\"print\",\"linkedin\");var hupso_counters_lang = \"fr_FR\";var hupso_image_folder_url = \"\";var hupso_twitter_via=\"BenoitRiviere14\";var hupso_url_c=\"\";var hupso_title_c=\"Alg%C3%A8bre%20de%20Boole%20%28ou%20arithm%C3%A9tique%20bool%C3%A9enne%29\";<\/script><script type=\"text\/javascript\" src=\"https:\/\/static.hupso.com\/share\/js\/counters.js\"><\/script><!-- Hupso Share Buttons --><\/div>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"ngg_post_thumbnail":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","_links_to":"","_links_to_target":""},"categories":[48,471,1326],"tags":[1831,2796,2498,1138,1835,848,2798,223,285,2797,1310,1821,1142,1830,1836,2774,1392,2011,222,847],"class_list":["post-10532","post","type-post","status-publish","format-standard","hentry","category-excel","category-langages","category-maitriser-excel","tag-algebre-de-boole","tag-arithmetique-booleenne","tag-comparaison","tag-criteres","tag-et","tag-false","tag-filtre","tag-if-then-elseif","tag-iif","tag-logique","tag-multicritere","tag-operateurs-booleens","tag-operateurs-de-comparaison","tag-operateurs-logiques","tag-ou","tag-recherchex","tag-si","tag-si-conditions","tag-tests-conditionnels","tag-true"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":false,"_links":{"self":[{"href":"https:\/\/www.auditsi.eu\/index.php?rest_route=\/wp\/v2\/posts\/10532","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.auditsi.eu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.auditsi.eu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.auditsi.eu\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.auditsi.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=10532"}],"version-history":[{"count":4,"href":"https:\/\/www.auditsi.eu\/index.php?rest_route=\/wp\/v2\/posts\/10532\/revisions"}],"predecessor-version":[{"id":10535,"href":"https:\/\/www.auditsi.eu\/index.php?rest_route=\/wp\/v2\/posts\/10532\/revisions\/10535"}],"wp:attachment":[{"href":"https:\/\/www.auditsi.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10532"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.auditsi.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10532"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.auditsi.eu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10532"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}