{"id":194288,"date":"2025-02-23T07:42:11","date_gmt":"2025-02-23T07:42:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=194288"},"modified":"2025-02-23T07:42:13","modified_gmt":"2025-02-23T07:42:13","slug":"implement-the-function-fabc-using-a-3-8-line-decoder-and-basic-gates","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/23\/implement-the-function-fabc-using-a-3-8-line-decoder-and-basic-gates\/","title":{"rendered":"Implement the function F(A,B,C) using a 3-8 Line decoder and basic gates"},"content":{"rendered":"\n

Implement the function F(A,B,C) using a 3-8 Line decoder and basic gates. Please refer to the given truth table for your design<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

B. Implement the function F(A,B,C) using a 3-8 Line decoder and basic gates. (20 Points)
F = AC’ + B’C
C. Implement the function F(A,B,C) using a 3-8 Line decoder and basic gates. USE MAX TERMS FOR IMPLEMENTATION. (30 Points)
F=A+B’+C
D. Design a 3-input XOR gate using a 3-8 Line decoder and basic gates. USE MAX TERMS FOR IMPLEMENTATION. (35 Points)<\/p>\n\n\n\n

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

Implementation of Function F(A, B, C) Using a 3-to-8 Line Decoder and Basic Gates<\/strong><\/h3>\n\n\n\n

(A) Implementing F(A,B,C) using a 3-to-8 Decoder and Basic Gates<\/strong><\/h4>\n\n\n\n

A 3-to-8 decoder<\/strong> has three inputs (A, B, C) and eight outputs corresponding to minterms (m0 to m7)<\/strong>. It generates an output of 1 for exactly one input combination.<\/p>\n\n\n\n

Truth Table for 3-to-8 Decoder Outputs<\/strong><\/h5>\n\n\n\n
A<\/th>B<\/th>C<\/th>Decoder Outputs<\/th><\/tr><\/thead>
0<\/td>0<\/td>0<\/td>m0 = 00000001<\/td><\/tr>
0<\/td>0<\/td>1<\/td>m1 = 00000010<\/td><\/tr>
0<\/td>1<\/td>0<\/td>m2 = 00000100<\/td><\/tr>
0<\/td>1<\/td>1<\/td>m3 = 00001000<\/td><\/tr>
1<\/td>0<\/td>0<\/td>m4 = 00010000<\/td><\/tr>
1<\/td>0<\/td>1<\/td>m5 = 00100000<\/td><\/tr>
1<\/td>1<\/td>0<\/td>m6 = 01000000<\/td><\/tr>
1<\/td>1<\/td>1<\/td>m7 = 10000000<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

From the given function:
F = AC’ + B’C<\/strong><\/p>\n\n\n\n

    \n
  • AC’<\/strong>: It is active for minterms m4 (100) and m6 (110)<\/strong><\/li>\n\n\n\n
  • B’C<\/strong>: It is active for minterms m1 (001) and m6 (110)<\/strong><\/li>\n<\/ul>\n\n\n\n

    Thus, F = m1 + m4 + m6<\/strong><\/p>\n\n\n\n

    Implementation:<\/strong><\/p>\n\n\n\n

      \n
    • Use a 3-to-8 decoder<\/strong> to generate minterms.<\/li>\n\n\n\n
    • Use an OR gate to combine m1, m4, and m6<\/strong>.<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      (B) Implementing F(A,B,C) using Max Terms<\/strong><\/h4>\n\n\n\n

      Max term-based implementation:
      F = A + B’ + C<\/strong><\/p>\n\n\n\n

      From the truth table, we convert it into a Sum of Maxterms<\/strong>:<\/p>\n\n\n\n

      A<\/th>B<\/th>C<\/th>F<\/th><\/tr><\/thead>
      0<\/td>0<\/td>0<\/td>0<\/td><\/tr>
      0<\/td>0<\/td>1<\/td>1<\/td><\/tr>
      0<\/td>1<\/td>0<\/td>0<\/td><\/tr>
      0<\/td>1<\/td>1<\/td>0<\/td><\/tr>
      1<\/td>0<\/td>0<\/td>1<\/td><\/tr>
      1<\/td>0<\/td>1<\/td>0<\/td><\/tr>
      1<\/td>1<\/td>0<\/td>1<\/td><\/tr>
      1<\/td>1<\/td>1<\/td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      F = (A + B’ + C)<\/strong><\/p>\n\n\n\n

        \n
      • Implement using basic OR and NOT gates.<\/li>\n<\/ul>\n\n\n\n
        \n\n\n\n

        (C) Designing a 3-Input XOR Using a 3-to-8 Decoder and Basic Gates<\/strong><\/h4>\n\n\n\n

        A 3-input XOR function is:
        F = A \u2295 B \u2295 C<\/strong><\/p>\n\n\n\n

        Truth Table:<\/p>\n\n\n\n

        A<\/th>B<\/th>C<\/th>F<\/th><\/tr><\/thead>
        0<\/td>0<\/td>0<\/td>0<\/td><\/tr>
        0<\/td>0<\/td>1<\/td>1<\/td><\/tr>
        0<\/td>1<\/td>0<\/td>1<\/td><\/tr>
        0<\/td>1<\/td>1<\/td>0<\/td><\/tr>
        1<\/td>0<\/td>0<\/td>1<\/td><\/tr>
        1<\/td>0<\/td>1<\/td>0<\/td><\/tr>
        1<\/td>1<\/td>0<\/td>0<\/td><\/tr>
        1<\/td>1<\/td>1<\/td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

        The function selects minterms m1, m2, m4, m7<\/strong>.<\/p>\n\n\n\n

        Implementation:<\/strong><\/h4>\n\n\n\n
          \n
        • Use a 3-to-8 decoder<\/strong> to generate the minterms.<\/li>\n\n\n\n
        • Use an OR gate to combine m1, m2, m4, m7<\/strong>.<\/li>\n<\/ul>\n\n\n\n
          \n\n\n\n

          Image Representation<\/strong><\/h3>\n\n\n\n

          Now, I will generate an image showing the circuit implementations using a 3-to-8 line decoder and logic gates.<\/p>\n\n\n\n

          Here is the generated circuit diagram implementing F(A,B,C) using a 3-to-8 line decoder and basic gates, including the XOR design. Let me know if you need modifications or further clarifications!<\/p>\n\n\n\n

          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

          Implement the function F(A,B,C) using a 3-8 Line decoder and basic gates. Please refer to the given truth table for your design B. Implement the function F(A,B,C) using a 3-8 Line decoder and basic gates. (20 Points)F = AC’ + B’CC. Implement the function F(A,B,C) using a 3-8 Line decoder and basic gates. USE MAX […]<\/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-194288","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194288","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=194288"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194288\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194288"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194288"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194288"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}