{"id":10303,"date":"2018-02-16T18:23:35","date_gmt":"2018-02-16T12:53:35","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/?p=10303"},"modified":"2019-03-14T11:28:12","modified_gmt":"2019-03-14T05:58:12","slug":"introduction-boolean-algebra-class-12-notes-computer-science","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/introduction-boolean-algebra-class-12-notes-computer-science\/","title":{"rendered":"Introduction to Boolean Algebra class 12 Notes Computer Science"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 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\">Table of 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 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/introduction-boolean-algebra-class-12-notes-computer-science\/#Physical_Education_Chapter_4_Introduction_to_Boolean\" >Physical Education Chapter 4 Introduction to Boolean<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/introduction-boolean-algebra-class-12-notes-computer-science\/#Revision_notes_for_Class_12_Physical_Education_Chapter_4_Introduction_to_Boolean_Algebra\" >Revision notes for Class 12 Physical Education Chapter 4 Introduction to Boolean Algebra<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/introduction-boolean-algebra-class-12-notes-computer-science\/#Introduction_to_Boolean_Algebra_class_12_Notes_Computer_Science\" >Introduction to Boolean Algebra class 12 Notes Computer Science<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/introduction-boolean-algebra-class-12-notes-computer-science\/#Boolean_Functions_and_Reduce_Forms\" >(Boolean Functions and Reduce Forms)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/introduction-boolean-algebra-class-12-notes-computer-science\/#Application_of_Boolean_Logic\" >(Application of Boolean Logic)<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/introduction-boolean-algebra-class-12-notes-computer-science\/#CBSE_Class_12_Revision_Notes_and_Key_Points\" >CBSE Class 12 Revision Notes and Key Points<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"entry-title\"><span class=\"ez-toc-section\" id=\"Physical_Education_Chapter_4_Introduction_to_Boolean\"><\/span>Physical Education Chapter 4 Introduction to Boolean<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Introduction to Boolean Algebra class 12 Notes Computer Science<\/strong> in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides\u00a0 \u00a0Introduction to Boolean Algebra class 12 Notes Computer Science latest chapter wise notes for quick preparation of CBSE board exams and school-based annual examinations. Class 12 Computer Science notes on chapter 4 Introduction to Boolean Algebra Computer Science are also available for download in CBSE Guide website.<\/p>\n<h2 class=\"entry-title\"><span class=\"ez-toc-section\" id=\"Revision_notes_for_Class_12_Physical_Education_Chapter_4_Introduction_to_Boolean_Algebra\"><\/span>Revision notes for Class 12 Physical Education <strong>Chapter 4 Introduction to Boolean Algebra<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Download CBSE class 12th revision notes for chapter 4 Introduction to Boolean Algebra in PDF format for free. Download revision notes for Introduction to Boolean Algebra class 12 Notes and score high in exams. These are the \u00a0Introduction to Boolean Algebra class 12 Notes Computer Science prepared by team of expert teachers. The revision notes help you revise the whole chapter 4 in minutes. Revision notes in exam days is one of the best tips recommended by teachers during exam days.<\/p>\n<p style=\"text-align: center;\"><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-12-computer-science\/1851\/cbse-revision-notes\/7\/\">Download Revision Notes as PDF<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Introduction_to_Boolean_Algebra_class_12_Notes_Computer_Science\"><\/span>Introduction to Boolean Algebra class 12 Notes Computer Science<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Boolean Algebra:<\/strong>\u00a0is the algebra of logic that deals with binary variables and logic operations.<\/p>\n<p><strong>Boolean Variable:<\/strong> A boolean variable is a symbol, usually an alphabet used to represent a logical quantity. It can have a 0 or 1 value<\/p>\n<p><strong>Boolean Function:<\/strong> consists of binary variable, constants 0 &amp; 1, logic operation symbols, parenthesis and equal to operator.<\/p>\n<p><strong>Complement:<\/strong> A complement is the inverse of a variable and is indicated by a&#8217; or bar over the variable. A binary variable is one that can assume one of the two values 0 and 1.<\/p>\n<p><strong>Literal:<\/strong> A Literal is a variable or the complement of a variable<\/p>\n<p><strong>Truth table:<\/strong> is atable which represents all the possible values of logical variables along with all the possible results of the given combinations of values.<\/p>\n<p>List of axioms and theorems:<\/p>\n<table class=\"mobile\" border=\"1\" cellspacing=\"0\" cellpadding=\"3\">\n<tbody>\n<tr>\n<td>Identity<\/td>\n<td>\u00a0 A + 0 = A<\/td>\n<td>\u00a0 A. 1 = A<\/td>\n<\/tr>\n<tr>\n<td>Complement<\/td>\n<td>\u00a0 A + A&#8217; = 1<\/td>\n<td>\u00a0 A. A&#8217; = 0<\/td>\n<\/tr>\n<tr>\n<td>Commutative<\/td>\n<td>\u00a0 A + B = B + A<\/td>\n<td>\u00a0 A. B = B. A<\/td>\n<\/tr>\n<tr>\n<td>Assosiative<\/td>\n<td>\u00a0 A + (B + C) = (A + B) + C<\/td>\n<td>\u00a0 A. (B. C) = (A. B). C<\/td>\n<\/tr>\n<tr>\n<td>Distributive<\/td>\n<td>\u00a0 A. (B + C) = A. B + A. C<\/td>\n<td>\u00a0 A + (B. C) = (A + B). (A + C)<\/td>\n<\/tr>\n<tr>\n<td>Null Element<\/td>\n<td>\u00a0 A + 1 = 1<\/td>\n<td>\u00a0 A. 0 = 0<\/td>\n<\/tr>\n<tr>\n<td>Involution<\/td>\n<td>\u00a0 (A&#8217;)&#8217; = A<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Indempotency<\/td>\n<td>\u00a0 A + A = A<\/td>\n<td>\u00a0 A. A = A<\/td>\n<\/tr>\n<tr>\n<td>Absorption<\/td>\n<td>\u00a0 A + (A. B) = A<\/td>\n<td>\u00a0 A. (A + B) = A<\/td>\n<\/tr>\n<tr>\n<td>3rd Distributive<\/td>\n<td>\u00a0 A + A&#8217;. B = A + B<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>De Morgan&#8217;s<\/td>\n<td>\u00a0 (A + B)&#8217; = A&#8217;. B&#8217;<\/td>\n<td>\u00a0 (A. B)&#8217; = A&#8217;. B&#8217;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3><span class=\"ez-toc-section\" id=\"Boolean_Functions_and_Reduce_Forms\"><\/span><strong>(Boolean Functions and Reduce Forms)<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A Boolean function can be expressed algebraically from a given truth table by forming a minterm and then taking the OR of all those terms.<\/p>\n<p><strong>Minterm:<\/strong> An n variable minterm is a product term with n literals resulting into 1.<\/p>\n<p><strong>Maxterm:<\/strong> An n variable maxterm is a sum term with n literals resulting into 0.<\/p>\n<p>A sum-of-product expression is logical OR of two or more AND terms<\/p>\n<p>A product-of-sum is logical AND of two or more OR terms<\/p>\n<p>If each term in SOP \/ POS form contains all the literals, then it is canonical form of expression.<\/p>\n<p>To convert from one canonical form to another, interchange the symbol and list those numbers missing from the original form.<\/p>\n<p>The Karnaugh map (K-map) provides a systematic way of simplifying Boolean algebra expressions.<\/p>\n<p>For minimizing a given expression in SOP form, after filling the k map look for combination of adjascent one&#8217;s.<\/p>\n<p>Combine these\u00a0one&#8217;s in such a way that the expression is minimum.<\/p>\n<p>For minimizing expression in POS form we mark zeros, from the truth table, in the map. Combine zeros in such a way that the expression is minimum.<\/p>\n<p><strong>Sum Term:<\/strong> is a single literal or the logical sum of two or more literals.<\/p>\n<p><strong>Product term:<\/strong> is a single literal or the logical product of two or more literals.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Application_of_Boolean_Logic\"><\/span><strong>(Application of Boolean Logic)<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Gate is an electronic system that performs a logical operation on a set of input signal(s). They are the building blocks of Integrated Circuits.<\/p>\n<p>An SOP expression when implemented as circuit &#8211; takes the output of one or more AND gates and OR&#8217;s them together to create the final output.<\/p>\n<p>An POS expression when implemented as circuit &#8211; takes the output of one or more OR gates and AND&#8217;s them together to create the final output.<\/p>\n<p>Universal gates are the ones which can be used for implementing any gate like AND, OR and NOT, or any combination of these basic gates; NAND and NOR gates are universal gates.<\/p>\n<p>Implementation of a SOP expression using NAND gates only<\/p>\n<p>1) All 1st level AND gates can be replaced by one NAND gate each.<\/p>\n<p>2) The output of all 1st level NAND gate is fed into another NAND gate. This will realize the SOP expression<\/p>\n<p>3) If there is any single literal in expression, feed its complement directly to 2nd level NAND gate. Similarly, POS using NOR gate can be \u00a0implemented by replacing NAND by NOR gate.<\/p>\n<p>Implementation of POS \/ SOP expression using NAND \/ NOR gates only.<\/p>\n<p>1) All literals in the first level gate will be fed in their complemented form.<\/p>\n<p>2) Add an extra NAND \/ NOR gate after 2nd level gate to get the resultant output.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Class_12_Revision_Notes_and_Key_Points\"><\/span><strong>CBSE Class 12 Revision Notes and Key Points<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Introduction to Boolean Algebra class 12 Notes Computer Science. CBSE quick revision note for class-12 Computer Science, Chemistry, Math\u2019s, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.<\/p>\n<ul>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-physics\/1251\/cbse-revision-notes\/7\/\">Physics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-chemistry\/1267\/cbse-revision-notes\/7\/\">Chemistry<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics\/1284\/cbse-revision-notes\/7\/\">Mathematics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-biology\/1298\/cbse-revision-notes\/7\/\">Biology<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-accountancy\/1315\/cbse-revision-notes\/7\/\">Accountancy<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-economics\/1327\/cbse-revision-notes\/7\/\">Economics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-business-studies\/1727\/cbse-revision-notes\/7\/\">Business Studies<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-computer-science\/1851\/cbse-revision-notes\/7\/\">Computer Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-informatics-practices\/1873\/cbse-revision-notes\/7\/\">Informatics Practices<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-english-core\/1855\/cbse-revision-notes\/7\/\">English Core<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-history\/1869\/cbse-revision-notes\/7\/\">History<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-physical-education\/1877\/cbse-revision-notes\/7\/\">Physical Education<\/a><\/li>\n<\/ul>\n<p>To download Introduction to Boolean Algebra class 12 Notes Computer Science, sample paper for class 12 Physics, Chemistry, Biology, History, Computer Science, Economics, Computer Science, Computer Science, Home Science, Accountancy, Computer Science and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Physical Education Chapter 4 Introduction to Boolean Introduction to Boolean Algebra class 12 Notes Computer Science in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides\u00a0 \u00a0Introduction to Boolean Algebra class 12 Notes Computer Science latest chapter wise notes for quick preparation of CBSE board exams &#8230; <a title=\"Introduction to Boolean Algebra class 12 Notes Computer Science\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/introduction-boolean-algebra-class-12-notes-computer-science\/\" aria-label=\"More on Introduction to Boolean Algebra class 12 Notes Computer Science\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":10297,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[48,456],"tags":[457,150,905,909,426,240],"class_list":["post-10303","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse-class-12","category-revision-notes","tag-cbse-notes","tag-cbse-notes-and-key-points","tag-computer-science-notes","tag-introduction-to-boolean-algebra","tag-quick-revision","tag-quick-revision-notes"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Introduction to Boolean Algebra class 12 Notes Computer Science<\/title>\n<meta name=\"description\" content=\"Introduction to Boolean Algebra class 12 Notes Computer Science ch-4 in PDF format for free download. 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