{"id":12479,"date":"2021-11-30T13:43:59","date_gmt":"2021-11-30T12:43:59","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=12479"},"modified":"2024-02-11T16:27:26","modified_gmt":"2024-02-11T15:27:26","slug":"algebre-de-boole","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/logic-math-27\/boole-algebra-865547\/","title":{"rendered":"3 Corrected exercises on Boolean Algebra"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"12479\" class=\"elementor elementor-12479\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f5366aa elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f5366aa\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column 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page<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b1cf564\" data-id=\"b1cf564\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d6c113b elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"d6c113b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Alg%C3%A8bre_de_Boole_(logique)\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Wiki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2f025dd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2f025dd\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-88574ae\" data-id=\"88574ae\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-424653c elementor-widget elementor-widget-heading\" data-id=\"424653c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/en\/logic-math-27\/boole-algebra-865547\/#Exercices-corriges-sur-Algebre-de-Boole-et-tableau-de-Karnaugh\" >Corrected exercises on Boolean algebra and Karnaugh table<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/complex-systems-ai.com\/en\/logic-math-27\/boole-algebra-865547\/#Exercice-1\" >Exercise 1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/complex-systems-ai.com\/en\/logic-math-27\/boole-algebra-865547\/#Exercice-2\" >Exercise 2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/complex-systems-ai.com\/en\/logic-math-27\/boole-algebra-865547\/#Exercice-3\" >Exercise 3<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercices-corriges-sur-Algebre-de-Boole-et-tableau-de-Karnaugh\"><\/span>Corrected exercises on Boolean algebra and Karnaugh table<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4299951 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4299951\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a566634\" data-id=\"a566634\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ed94261 elementor-widget elementor-widget-text-editor\" data-id=\"ed94261\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>This tutorial offers corrected exercises on Boolean algebra and Karnaugh diagrams or tables.<\/p><p><img decoding=\"async\" class=\"aligncenter wp-image-11096 size-full\" src=\"http:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/cropped-Capture.png\" alt=\"Boolean algebra\" width=\"97\" height=\"97\" title=\"\"><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-0519044 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0519044\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a17faf9\" data-id=\"a17faf9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-83eacc4 elementor-widget elementor-widget-heading\" data-id=\"83eacc4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-1\"><\/span>Exercise 1<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-22e124d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"22e124d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4cd1fb0\" data-id=\"4cd1fb0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6995ba0 elementor-widget elementor-widget-text-editor\" data-id=\"6995ba0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The K-Gaz company decides to recruit employees internally for its subsidiary.<\/p><p>For each employee, we define the following Boolean variables:<\/p><ul><li>a = 1 if he has more than 5 years of seniority in the company<\/li><li>b = 1 if he has a BTS-IG<\/li><li>c = 1 if he speaks fluent English<\/li><\/ul><p>The human resources department decides that employees can apply:<\/p><ul><li>\u00a0that meet the three conditions<\/li><li>\u00a0or who have less than 5 years of seniority but who master English<\/li><li>or who do not speak English who have a BTS-IG<\/li><\/ul><p>Here are the questions:<\/p><ol><li>Give the HR criteria in Boolean expression<\/li><li>Represent the expression by a Karnaugh array<\/li><li>Simplify it<\/li><li>Find the result by calculation using backspace<\/li><li>Conclude on the simplified version<\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-60bad68 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"60bad68\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-87fc7ec\" data-id=\"87fc7ec\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-dad9967 elementor-widget elementor-widget-toggle\" data-id=\"dad9967\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2291\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2291\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2291\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2291\"><p>Question 1<\/p><p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-12482 size-large\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole1-1024x183.png\" alt=\"Karnaugh boolean algebra\" width=\"1024\" height=\"183\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole1-1024x183.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole1-300x53.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole1-768x137.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole1.png 1066w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p><p>Question 2<\/p><p>We mark a 1 each time an element of the Boolean expression is true.<\/p><p><img decoding=\"async\" class=\"alignnone wp-image-12483 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole2.png\" alt=\"Karnaugh boolean algebra\" width=\"964\" height=\"137\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole2.png 964w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole2-300x43.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole2-768x109.png 768w\" sizes=\"(max-width: 964px) 100vw, 964px\" \/><\/p><p>Question 3<\/p><p>To simplify the expression, we look in the table at the squares of 4 elements or the rectangles of two elements (not necessarily connected) of which at most one literal changes between row and column.<\/p><p>For example, the green rectangle, only the literal b changes, so \u00e4c does not change (\u00e4 considering the row and c considering both columns). In the red square, in column, only b changes (a changes in rows, and c changes in column).<\/p><p>We deduce the simplified expression.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-12484 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole3.png\" alt=\"Karnaugh boolean algebra\" width=\"923\" height=\"144\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole3.png 923w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole3-300x47.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole3-768x120.png 768w\" sizes=\"(max-width: 923px) 100vw, 923px\" \/><\/p><p>Question 4<\/p><p>The technique of backtracking consists in going back little by little on the results according to the lack of computational element. For example, after factoring by b, we will have ac + C_barre. In view of the formula, it is obvious that ac + \u00e4c + c_barre would be necessary for this expression to be equal to 1.<\/p><p>Thus, each time that a computational element is missing to arrive at its finality, it is possible to transform the preceding calculation lines by adding already existing elements or by multiplying by 1 such as for example b + b_barre to reach its ends.<\/p><p>Here is the final reasoning:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-12485 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole4.png\" alt=\"Karnaugh boolean algebra\" width=\"398\" height=\"307\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole4.png 398w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole4-300x231.png 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><\/p><p>Question 5<\/p><p>Deduces from this that the HR accepts applicants who have a BTS-IG or who have less than 5 years of seniority but mastering English.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-effd0fc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"effd0fc\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9fc44bb\" data-id=\"9fc44bb\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0b99ce3 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"0b99ce3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-16d44c8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"16d44c8\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d3f3845\" data-id=\"d3f3845\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8eef849 elementor-widget elementor-widget-heading\" data-id=\"8eef849\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-2\"><\/span>Exercise 2<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c237973 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c237973\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b64cadf\" data-id=\"b64cadf\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-077102e elementor-widget elementor-widget-text-editor\" data-id=\"077102e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The person in charge of the computer park of a company considers the acquisition of new computers. To equip himself, this manager goes to a computer equipment sales company that offers predefined configurations (computer and peripherals).<\/p><p>We define the criteria:<br \/>a: the configuration includes a DVD burner;<br \/>b: the configuration includes a printer;<br \/>c: the configuration includes a scanner.<\/p><p>Equipment constraints exclude the configuration with a DVD burner but without a scanner, as well as the configurations without a burner and without a printer.<\/p><p>Here are the questions:<\/p><ol><li>Give the Boolean expression E translating the exclusion conditions<\/li><li>Set the Karnaugh table of E<\/li><li>Translate and say if a (b_barre) c is accepted<\/li><li>Determine an expression of F reflecting the acceptance conditions.<\/li><li>Translate the simplified version of F.<\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c487aee elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c487aee\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-872e128\" data-id=\"872e128\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4c26fc1 elementor-widget elementor-widget-toggle\" data-id=\"4c26fc1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-7981\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-7981\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-7981\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-7981\"><p>1- The expression is E = a (c_barre) + \u00e4 (b_barre)<\/p><p>2- The Karnaugh table of E is\u00a0<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-12486 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole5.png\" alt=\"Karnaugh boolean algebra\" width=\"529\" height=\"76\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole5.png 529w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole5-300x43.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><\/p><p>3- the expression means equipped with a DVD burner and a scanner but without a printer. She is not present in E&#039;s Karnaugh so she is allowed<\/p><p>4- Here is the Karnaugh of E<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-12487 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole6.png\" alt=\"Karnaugh boolean algebra\" width=\"388\" height=\"122\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole6.png 388w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/boole6-300x94.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/p><p>In green c varies. In red b varies.<\/p><p>5- The simplified expression gives either an engraver and a scanner; or no burner and printer.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-aca5c14 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"aca5c14\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-cf8282c\" data-id=\"cf8282c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6a9a8aa elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"6a9a8aa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5c5a5c1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5c5a5c1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2471724\" data-id=\"2471724\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f9cdc30 elementor-widget elementor-widget-heading\" data-id=\"f9cdc30\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exercice-3\"><\/span>Exercise 3<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a154fed elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a154fed\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8b1a069\" data-id=\"8b1a069\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e9ca458 elementor-widget elementor-widget-text-editor\" data-id=\"e9ca458\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The director of human resources (HRD) of a town hall must recruit a person for a job concerning the circulation of cars in the city center.<\/p><p>To make his choice, the HRD sets up three selection criteria concerning knowledge in computer science, experience in the field concerned and the follow-up of a specific training course.<\/p><p>The recruited person must:<\/p><ul><li>have computer knowledge and experience in the relevant field;<\/li><li>or not have computer knowledge, but have followed a specific training course;<\/li><li>or not have experience in the field concerned, but have followed a specific training course.<\/li><\/ul><p>We define the following three Boolean variables a, b and c:<\/p><ul><li>a = 1 if the person has computer knowledge, a = 0 otherwise;<\/li><li>b = 1 if the person has experience in the field concerned, b = 0 otherwise;<\/li><li>c = 1 if the person has followed a specific training course, c = 0 otherwise.<\/li><\/ul><p>Here are the questions:<\/p><ol><li>Describe the situation corresponding to the product ab \/ c<\/li><li>Define the Boolean expression E corresponding to the HRD selection criteria.<\/li><li>Find a simplified writing of the Boolean expression E.<\/li><li>Explain the simplified version.<\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-722f0a2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"722f0a2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-55ada19\" data-id=\"55ada19\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ff65cdb elementor-widget elementor-widget-toggle\" data-id=\"ff65cdb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2671\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2671\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Solution<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2671\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2671\"><p>1- ab \/ c means that the person has computer knowledge (a = 1) and experience in the field concerned (b = 1), but has not followed a specific training course (c = 0).<\/p><p>2- E = ab + \/ ac + bc<\/p><p>3- Karnaugh&#039;s table and its simplified model is as follows<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-12497 size-medium\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/FLX-Karnaugh-300x157.jpg\" alt=\"Karnaugh boolean algebra\" width=\"300\" height=\"157\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/FLX-Karnaugh-300x157.jpg 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/FLX-Karnaugh-768x402.jpg 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2021\/11\/FLX-Karnaugh.jpg 878w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p>4- This means: The person has computer knowledge (a = 1) and experience in the field concerned (b = 1) OR has followed a specific training course (c = 1).<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Mathematics Home page Wiki Corrected exercises on Boolean algebra and Karnaugh table This tutorial offers corrected exercises on Boolean algebra and\u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":12320,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-12479","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/12479","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/comments?post=12479"}],"version-history":[{"count":7,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/12479\/revisions"}],"predecessor-version":[{"id":20278,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/12479\/revisions\/20278"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/12320"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=12479"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}