{"id":186533,"date":"2025-01-25T08:54:38","date_gmt":"2025-01-25T08:54:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=186533"},"modified":"2025-01-25T08:54:42","modified_gmt":"2025-01-25T08:54:42","slug":"f-abc-abc-abc-truth-table","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/25\/f-abc-abc-abc-truth-table\/","title":{"rendered":"F = A\u2019B\u2019C\u2019 + A\u2019BC\u2019 + ABC\u2019 truth table"},"content":{"rendered":"\n

F = A\u2019B\u2019C\u2019 + A\u2019BC\u2019 + ABC\u2019 truth table<\/p>\n\n\n\n

kmap<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To find the simplified Boolean expression for the given equation ( F = A’B’C’ + A’BC’ + ABC’ ), we can follow these steps:<\/p>\n\n\n\n

1. Construct the Truth Table<\/h3>\n\n\n\n

We first construct a truth table to evaluate the expression ( F = A’B’C’ + A’BC’ + ABC’ ). The variables involved are ( A ), ( B ), and ( C ), and each combination of these variables gives a different output for the function ( F ).<\/p>\n\n\n\n

A<\/th>B<\/th>C<\/th>A’B’C’<\/th>A’BC’<\/th>ABC’<\/th>F (A’B’C’ + A’BC’ + ABC’)<\/th><\/tr><\/thead>
0<\/td>0<\/td>0<\/td>1<\/td>0<\/td>0<\/td>1<\/td><\/tr>
0<\/td>0<\/td>1<\/td>0<\/td>0<\/td>0<\/td>0<\/td><\/tr>
0<\/td>1<\/td>0<\/td>1<\/td>1<\/td>0<\/td>1<\/td><\/tr>
0<\/td>1<\/td>1<\/td>0<\/td>0<\/td>0<\/td>0<\/td><\/tr>
1<\/td>0<\/td>0<\/td>0<\/td>0<\/td>1<\/td>1<\/td><\/tr>
1<\/td>0<\/td>1<\/td>0<\/td>0<\/td>0<\/td>0<\/td><\/tr>
1<\/td>1<\/td>0<\/td>0<\/td>0<\/td>1<\/td>1<\/td><\/tr>
1<\/td>1<\/td>1<\/td>0<\/td>0<\/td>0<\/td>0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

2. K-map (Karnaugh Map) Method<\/h3>\n\n\n\n

Next, we use a Karnaugh map to simplify the expression. A Karnaugh map is a graphical method of simplifying Boolean functions. Here’s the K-map for 3 variables:<\/p>\n\n\n\n

AB \\ C<\/th>0<\/th>1<\/th><\/tr><\/thead>
00<\/td>1<\/td>0<\/td><\/tr>
01<\/td>1<\/td>0<\/td><\/tr>
11<\/td>1<\/td>0<\/td><\/tr>
10<\/td>0<\/td>0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

3. Simplification<\/h3>\n\n\n\n

From the K-map, we can group the 1s into the smallest number of groups. We observe the following:<\/p>\n\n\n\n

    \n
  • There is a group of two 1s in the first column (where ( C = 0 ) and ( A’B’ ) and ( A’B ) are the conditions).<\/li>\n\n\n\n
  • There is a group of two 1s in the second row.<\/li>\n<\/ul>\n\n\n\n

    The simplified Boolean expression from this grouping is ( F = A’C’ + BC’ ).<\/p>\n\n\n\n

    4. Final Answer<\/h3>\n\n\n\n

    The simplified Boolean expression for the given function is ( F = A’C’ + BC’ ).<\/p>\n\n\n\n

    Explanation<\/h3>\n\n\n\n
      \n
    1. Truth Table<\/strong>: The truth table evaluates the original equation for all combinations of the variables ( A ), ( B ), and ( C ). This ensures that we account for all possible scenarios.<\/li>\n\n\n\n
    2. K-map<\/strong>: The K-map technique allows us to visually identify which terms can be grouped together and eliminated to simplify the Boolean expression. By identifying the patterns in the K-map, we reduce the original function to a more manageable form.<\/li>\n\n\n\n
    3. Simplification<\/strong>: The simplification process reduces the expression from three terms to two terms. By using a Karnaugh map, we can make the expression more efficient and easier to implement in logic circuits.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

      F = A\u2019B\u2019C\u2019 + A\u2019BC\u2019 + ABC\u2019 truth table kmap The Correct Answer and Explanation is : To find the simplified Boolean expression for the given equation ( F = A’B’C’ + A’BC’ + ABC’ ), we can follow these steps: 1. Construct the Truth Table We first construct a truth table to evaluate the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-186533","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186533","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=186533"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/186533\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=186533"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=186533"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=186533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}