{"id":1060,"date":"2020-10-29T03:02:21","date_gmt":"2020-10-29T03:02:21","guid":{"rendered":"http:\/\/learnlearn.uk\/alevelcs\/?page_id=1060"},"modified":"2020-11-02T02:39:37","modified_gmt":"2020-11-02T02:39:37","slug":"boolean-simplification-examples","status":"publish","type":"page","link":"https:\/\/learnlearn.uk\/alevelcs\/boolean-simplification-examples\/","title":{"rendered":"Boolean Simplification Examples"},"content":{"rendered":"<p>[latexpage]<\/p>\n<div class=\"responsive-tabs\">\n<h2 class=\"tabtitle\">1<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Example 1<\/h3>\n<p>Simplify the following Boolean Algebra:<\/p>\n<p>$(A.\\overline{A} )+B$<\/p>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>hint<\/div><div class=\"arconix-toggle-content\">\n<ul>\n<li>Complement Rule<\/li>\n<li>Identity Rule<\/li>\n<\/ul>\n<\/div><\/div>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>Solution<\/div><div class=\"arconix-toggle-content\">\n<p>$(A.\\overline{A} )+B$<\/p>\n<p>$(0)+B$#Complement<\/p>\n<p>$B$ #Identity<\/p>\n<\/div><\/div>\n\n<\/div><h2 class=\"tabtitle\">2<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Example 2<\/h3>\n<p>$(A.B)+(\\overline{A}.B)$<\/p>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>hint<\/div><div class=\"arconix-toggle-content\">\n<p>Absorption<\/p>\n<\/div><\/div>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>Solution<\/div><div class=\"arconix-toggle-content\">\n<p>$(A.B)+(\\overline{A}.B)$ #Absorption<\/p>\n<p>B<\/p>\n<\/div><\/div>\n\n<\/div><h2 class=\"tabtitle\">3<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Example 3<\/h3>\n<p>$(A+B).(A+C)$<\/p>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>hint<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>Solution<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n\n<\/div><h2 class=\"tabtitle\">4<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Example 4<\/h3>\n<p>$(\\overline{A} + B).(A+B)$<\/p>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>hint<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>Solution<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n\n<\/div><h2 class=\"tabtitle\">5<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Example 5<\/h3>\n<p>$A\\overline{C} + ABC$<\/p>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>hint<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>Solution<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n\n<\/div><h2 class=\"tabtitle\">6<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Example 6<\/h3>\n<p>$A.\\overline{B}.D + A.\\overline{B}.\\overline{D}$<\/p>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>hint<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>Solution<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n\n<\/div><h2 class=\"tabtitle\">7<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Example 7<\/h3>\n<p>$B + B.C + A.C + A.B + A.C.B$<\/p>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>hint<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>Solution<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n\n<\/div><h2 class=\"tabtitle\">8<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Example 8<\/h3>\n<p>$\\overline{A}.\\overline{B}.\\overline{C}.\\overline{D} +\u00a0\\overline{A}.\\overline{B}.\\overline{C}.D +\u00a0\\overline{A}.\\overline{B}.C.D+\\overline{A}.\\overline{B}.C.\\overline{D} +\u00a0\\overline{A}.B.\\overline{C}.\\overline{D} $<\/p>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>hint<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>Solution<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n\n<\/div><h2 class=\"tabtitle\">9<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Example 9<\/h3>\n<p>$\\overline{(\\overline{A}.(B+C))}$<\/p>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>hint<\/div><div class=\"arconix-toggle-content\">\n<ul>\n<li>Use De Morgan&#8217;s Law<\/li>\n<li>Use Involution Law(Double Inversion)<\/li>\n<\/ul>\n<\/div><\/div>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>Solution<\/div><div class=\"arconix-toggle-content\">\n<p>$\\overline{(\\overline{A}.(B+C))}$ #Original Expression<\/p>\n<p>$(\\overline{\\overline{A}} + \\overline{(B + C))}$ #Use De Morgan&#8217;s law on the ANDed components<\/p>\n<p>$(A + \\overline{(B + C))}$\u00a0 Involution Law (Double negatives cancel)<\/p>\n<p>$(A + (\\overline{B}.\\overline{C}))$ De Morgan&#8217;s Law again<\/p>\n<p>$\\bf{A + \\overline{B}.\\overline{C}}$\u00a0 # BODMAS rules allow removal of brackets<\/p>\n<\/div><\/div>\n\n<\/div><h2 class=\"tabtitle\">10<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Example 10<\/h3>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>hint<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>Solution<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n\n<\/div><h2 class=\"tabtitle\">11<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Example 11<\/h3>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>hint<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n<div class=\"arconix-toggle-wrap\"><div class=\"arconix-toggle-title toggle-closed\"><i class='fa fa-plus-square'><\/i>Solution<\/div><div class=\"arconix-toggle-content\">\n<\/div><\/div>\n<p>&nbsp;<\/p>\n<\/div><\/div>\n<p>[latexpage]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[latexpage] Example 1 Simplify the following Boolean Algebra: $(A.\\overline{A} )+B$ Example 2 $(A.B)+(\\overline{A}.B)$ Example 3 $(A+B).(A+C)$ Example 4 $(\\overline{A} + B).(A+B)$ Example 5 $A\\overline{C} + ABC$ Example 6 $A.\\overline{B}.D + A.\\overline{B}.\\overline{D}$ Example 7 $B + B.C + A.C + A.B + A.C.B$ Example 8 $\\overline{A}.\\overline{B}.\\overline{C}.\\overline{D} +\u00a0\\overline{A}.\\overline{B}.\\overline{C}.D +\u00a0\\overline{A}.\\overline{B}.C.D+\\overline{A}.\\overline{B}.C.\\overline{D} +\u00a0\\overline{A}.B.\\overline{C}.\\overline{D} $ Example 9 $\\overline{(\\overline{A}.(B+C))}$ Example 10 Example&hellip;&nbsp;<a href=\"https:\/\/learnlearn.uk\/alevelcs\/boolean-simplification-examples\/\" class=\"\" rel=\"bookmark\">Read More &raquo;<span class=\"screen-reader-text\">Boolean Simplification Examples<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":70,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Boolean Simplification Examples - A Level Computer Science<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/learnlearn.uk\/alevelcs\/boolean-simplification-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" 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+\u00a0overline{A}.overline{B}.overline{C}.D +\u00a0overline{A}.overline{B}.C.D+overline{A}.overline{B}.C.overline{D} +\u00a0overline{A}.B.overline{C}.overline{D} $ Example 9 $overline{(overline{A}.(B+C))}$ Example 10 Example&hellip;&nbsp;Read More &raquo;Boolean Simplification Examples","og_url":"https:\/\/learnlearn.uk\/alevelcs\/boolean-simplification-examples\/","og_site_name":"A Level Computer Science","article_modified_time":"2020-11-02T02:39:37+00:00","twitter_card":"summary_large_image","twitter_misc":{"Estimated reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/learnlearn.uk\/alevelcs\/boolean-simplification-examples\/","url":"https:\/\/learnlearn.uk\/alevelcs\/boolean-simplification-examples\/","name":"Boolean Simplification Examples - A Level Computer 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Science"},"image":{"@id":"https:\/\/learnlearn.uk\/alevelcs\/#\/schema\/logo\/image\/"}}]}},"rttpg_featured_image_url":null,"rttpg_author":{"display_name":"learnlearnadmin","author_link":"https:\/\/learnlearn.uk\/alevelcs\/author\/learnlearnadmin\/"},"rttpg_comment":0,"rttpg_category":null,"rttpg_excerpt":"[latexpage] Example 1 Simplify the following Boolean Algebra: $(A.\\overline{A} )+B$ Example 2 $(A.B)+(\\overline{A}.B)$ Example 3 $(A+B).(A+C)$ Example 4 $(\\overline{A} + B).(A+B)$ Example 5 $A\\overline{C} + ABC$ Example 6 $A.\\overline{B}.D + A.\\overline{B}.\\overline{D}$ Example 7 $B + B.C + A.C + A.B + A.C.B$ Example 8 $\\overline{A}.\\overline{B}.\\overline{C}.\\overline{D} +\u00a0\\overline{A}.\\overline{B}.\\overline{C}.D +\u00a0\\overline{A}.\\overline{B}.C.D+\\overline{A}.\\overline{B}.C.\\overline{D} +\u00a0\\overline{A}.B.\\overline{C}.\\overline{D} $ Example 9 $\\overline{(\\overline{A}.(B+C))}$ Example 10 Example&hellip;&nbsp;Read&hellip;","_links":{"self":[{"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/pages\/1060"}],"collection":[{"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/comments?post=1060"}],"version-history":[{"count":33,"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/pages\/1060\/revisions"}],"predecessor-version":[{"id":1107,"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/pages\/1060\/revisions\/1107"}],"wp:attachment":[{"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/media?parent=1060"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}