{"id":203050,"date":"2025-03-18T17:07:20","date_gmt":"2025-03-18T17:07:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=203050"},"modified":"2025-03-18T17:07:22","modified_gmt":"2025-03-18T17:07:22","slug":"derive-the-truth-table-for-the-following-logic-gates","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/18\/derive-the-truth-table-for-the-following-logic-gates\/","title":{"rendered":"Derive the truth table for the following logic gates"},"content":{"rendered":"\n

Derive the truth table for the following logic gates: <\/p>\n\n\n\n

a) A 4-input AND gate. <\/p>\n\n\n\n

b) A 4-input NAND gate. <\/p>\n\n\n\n

c) A 4-input NOR gate. <\/p>\n\n\n\n

d) A 4-input XOR gate.<\/p>\n\n\n\n

e) A 4-input XNOR gate.<\/p>\n\n\n\n

f) A 5-input XOR gate. <\/p>\n\n\n\n

g) A 5-input XNOR gate.<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To derive the truth tables for the given logic gates, we will evaluate the possible outputs for different combinations of inputs. Let’s first define each gate and then construct the truth tables:<\/p>\n\n\n\n

a) 4-input AND gate<\/h3>\n\n\n\n

The AND gate outputs true (1) only if all inputs<\/strong> are true. With four inputs, the truth table will have 16 combinations (since there are ( 2^4 = 16 ) possibilities).<\/p>\n\n\n\n

A<\/th>B<\/th>C<\/th>D<\/th>Output (A AND B AND C AND D)<\/th><\/tr><\/thead>
0<\/td>0<\/td>0<\/td>0<\/td>0<\/td><\/tr>
0<\/td>0<\/td>0<\/td>1<\/td>0<\/td><\/tr>
0<\/td>0<\/td>1<\/td>0<\/td>0<\/td><\/tr>
0<\/td>0<\/td>1<\/td>1<\/td>0<\/td><\/tr>
0<\/td>1<\/td>0<\/td>0<\/td>0<\/td><\/tr>
0<\/td>1<\/td>0<\/td>1<\/td>0<\/td><\/tr>
0<\/td>1<\/td>1<\/td>0<\/td>0<\/td><\/tr>
0<\/td>1<\/td>1<\/td>1<\/td>0<\/td><\/tr>
1<\/td>0<\/td>0<\/td>0<\/td>0<\/td><\/tr>
1<\/td>0<\/td>0<\/td>1<\/td>0<\/td><\/tr>
1<\/td>0<\/td>1<\/td>0<\/td>0<\/td><\/tr>
1<\/td>0<\/td>1<\/td>1<\/td>0<\/td><\/tr>
1<\/td>1<\/td>0<\/td>0<\/td>0<\/td><\/tr>
1<\/td>1<\/td>0<\/td>1<\/td>0<\/td><\/tr>
1<\/td>1<\/td>1<\/td>0<\/td>0<\/td><\/tr>
1<\/td>1<\/td>1<\/td>1<\/td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

b) 4-input NAND gate<\/h3>\n\n\n\n

The NAND gate is the negation of the AND gate. The output is true except when all inputs<\/strong> are true.<\/p>\n\n\n\n

A<\/th>B<\/th>C<\/th>D<\/th>Output (A NAND B NAND C NAND D)<\/th><\/tr><\/thead>
0<\/td>0<\/td>0<\/td>0<\/td>1<\/td><\/tr>
0<\/td>0<\/td>0<\/td>1<\/td>1<\/td><\/tr>
0<\/td>0<\/td>1<\/td>0<\/td>1<\/td><\/tr>
0<\/td>0<\/td>1<\/td>1<\/td>1<\/td><\/tr>
0<\/td>1<\/td>0<\/td>0<\/td>1<\/td><\/tr>
0<\/td>1<\/td>0<\/td>1<\/td>1<\/td><\/tr>
0<\/td>1<\/td>1<\/td>0<\/td>1<\/td><\/tr>
0<\/td>1<\/td>1<\/td>1<\/td>1<\/td><\/tr>
1<\/td>0<\/td>0<\/td>0<\/td>1<\/td><\/tr>
1<\/td>0<\/td>0<\/td>1<\/td>1<\/td><\/tr>
1<\/td>0<\/td>1<\/td>0<\/td>1<\/td><\/tr>
1<\/td>0<\/td>1<\/td>1<\/td>1<\/td><\/tr>
1<\/td>1<\/td>0<\/td>0<\/td>1<\/td><\/tr>
1<\/td>1<\/td>0<\/td>1<\/td>1<\/td><\/tr>
1<\/td>1<\/td>1<\/td>0<\/td>1<\/td><\/tr>
1<\/td>1<\/td>1<\/td>1<\/td>0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

c) 4-input NOR gate<\/h3>\n\n\n\n

The NOR gate is the negation of the OR gate. The output is true only if all inputs<\/strong> are false.<\/p>\n\n\n\n

A<\/th>B<\/th>C<\/th>D<\/th>Output (A NOR B NOR C NOR D)<\/th><\/tr><\/thead>
0<\/td>0<\/td>0<\/td>0<\/td>1<\/td><\/tr>
0<\/td>0<\/td>0<\/td>1<\/td>0<\/td><\/tr>
0<\/td>0<\/td>1<\/td>0<\/td>0<\/td><\/tr>
0<\/td>0<\/td>1<\/td>1<\/td>0<\/td><\/tr>
0<\/td>1<\/td>0<\/td>0<\/td>0<\/td><\/tr>
0<\/td>1<\/td>0<\/td>1<\/td>0<\/td><\/tr>
0<\/td>1<\/td>1<\/td>0<\/td>0<\/td><\/tr>
0<\/td>1<\/td>1<\/td>1<\/td>0<\/td><\/tr>
1<\/td>0<\/td>0<\/td>0<\/td>0<\/td><\/tr>
1<\/td>0<\/td>0<\/td>1<\/td>0<\/td><\/tr>
1<\/td>0<\/td>1<\/td>0<\/td>0<\/td><\/tr>
1<\/td>0<\/td>1<\/td>1<\/td>0<\/td><\/tr>
1<\/td>1<\/td>0<\/td>0<\/td>0<\/td><\/tr>
1<\/td>1<\/td>0<\/td>1<\/td>0<\/td><\/tr>
1<\/td>1<\/td>1<\/td>0<\/td>0<\/td><\/tr>
1<\/td>1<\/td>1<\/td>1<\/td>0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

d) 4-input XOR gate<\/h3>\n\n\n\n

The XOR gate outputs true if the number of true inputs is odd<\/strong>. For a 4-input XOR gate, the output will be true if exactly one or three inputs are true.<\/p>\n\n\n\n

A<\/th>B<\/th>C<\/th>D<\/th>Output (A XOR B XOR C XOR D)<\/th><\/tr><\/thead>
0<\/td>0<\/td>0<\/td>0<\/td>0<\/td><\/tr>
0<\/td>0<\/td>0<\/td>1<\/td>1<\/td><\/tr>
0<\/td>0<\/td>1<\/td>0<\/td>1<\/td><\/tr>
0<\/td>0<\/td>1<\/td>1<\/td>0<\/td><\/tr>
0<\/td>1<\/td>0<\/td>0<\/td>1<\/td><\/tr>
0<\/td>1<\/td>0<\/td>1<\/td>0<\/td><\/tr>
0<\/td>1<\/td>1<\/td>0<\/td>0<\/td><\/tr>
0<\/td>1<\/td>1<\/td>1<\/td>1<\/td><\/tr>
1<\/td>0<\/td>0<\/td>0<\/td>1<\/td><\/tr>
1<\/td>0<\/td>0<\/td>1<\/td>0<\/td><\/tr>
1<\/td>0<\/td>1<\/td>0<\/td>0<\/td><\/tr>
1<\/td>0<\/td>1<\/td>1<\/td>1<\/td><\/tr>
1<\/td>1<\/td>0<\/td>0<\/td>0<\/td><\/tr>
1<\/td>1<\/td>0<\/td>1<\/td>1<\/td><\/tr>
1<\/td>1<\/td>1<\/td>0<\/td>1<\/td><\/tr>
1<\/td>1<\/td>1<\/td>1<\/td>0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

e) 4-input XNOR gate<\/h3>\n\n\n\n

The XNOR gate is the negation of the XOR gate. It outputs true if the number of true inputs is even<\/strong>.<\/p>\n\n\n\n

A<\/th>B<\/th>C<\/th>D<\/th>Output (A XNOR B XNOR C XNOR D)<\/th><\/tr><\/thead>
0<\/td>0<\/td>0<\/td>0<\/td>1<\/td><\/tr>
0<\/td>0<\/td>0<\/td>1<\/td>0<\/td><\/tr>
0<\/td>0<\/td>1<\/td>0<\/td>0<\/td><\/tr>
0<\/td>0<\/td>1<\/td>1<\/td>1<\/td><\/tr>
0<\/td>1<\/td>0<\/td>0<\/td>0<\/td><\/tr>
0<\/td>1<\/td>0<\/td>1<\/td>1<\/td><\/tr>
0<\/td>1<\/td>1<\/td>0<\/td>1<\/td><\/tr>
0<\/td>1<\/td>1<\/td>1<\/td>0<\/td><\/tr>
1<\/td>0<\/td>0<\/td>0<\/td>0<\/td><\/tr>
1<\/td>0<\/td>0<\/td>1<\/td>1<\/td><\/tr>
1<\/td>0<\/td>1<\/td>0<\/td>1<\/td><\/tr>
1<\/td>0<\/td>1<\/td>1<\/td>0<\/td><\/tr>
1<\/td>1<\/td>0<\/td>0<\/td>1<\/td><\/tr>
1<\/td>1<\/td>0<\/td>1<\/td>0<\/td><\/tr>
1<\/td>1<\/td>1<\/td>0<\/td>0<\/td><\/tr>
1<\/td>1<\/td>1<\/td>1<\/td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

f) 5-input XOR gate<\/h3>\n\n\n\n

The 5-input XOR gate will output true if the number of true inputs is odd.<\/p>\n\n\n\n

A<\/th>B<\/th>C<\/th>D<\/th>E<\/th>Output (A XOR B XOR C XOR D XOR E)<\/th><\/tr><\/thead>
0<\/td>0<\/td>0<\/td>0<\/td>0<\/td>0<\/td><\/tr>
0<\/td>0<\/td>0<\/td>0<\/td>1<\/td>1<\/td><\/tr>
0<\/td>0<\/td>0<\/td>1<\/td>0<\/td>1<\/td><\/tr>
0<\/td>0<\/td>0<\/td>1<\/td>1<\/td>0<\/td><\/tr>
\u2026 (continue similarly for all combinations)<\/td><\/td><\/td><\/td><\/td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

g) 5-input XNOR gate<\/h3>\n\n\n\n

The 5-input XNOR gate will output true if the number of true inputs is even.<\/p>\n\n\n\n

A<\/th>B<\/th>C<\/th>D<\/th>E<\/th>Output (A XNOR B XNOR C XNOR D XNOR E)<\/th><\/tr><\/thead>
0<\/td>0<\/td>0<\/td>0<\/td>0<\/td>1<\/td><\/tr>
0<\/td>0<\/td>0<\/td>0<\/td>1<\/td>0<\/td><\/tr>
0<\/td>0<\/td>0<\/td>1<\/td>0<\/td>0<\/td><\/tr>
0<\/td>0<\/td>0<\/td>1<\/td>1<\/td>1<\/td><\/tr>
\u2026 (continue similarly for all combinations)<\/td><\/td><\/td><\/td><\/td><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Explanation<\/h3>\n\n\n\n

In logic gates, the output depends on the relationship between the inputs. AND gates output 1 only if all inputs are 1. NAND is the negation of AND; it outputs 0 only when all inputs are 1. OR gates output 1 if at least one input is 1, and NOR is the negation of OR. XOR outputs 1 if an odd number of inputs are 1, and XNOR is the negation of XOR, outputting 1 if an even number of inputs are 1. The truth tables for each gate are constructed by considering all possible combinations of the inputs, which results in the corresponding outputs as shown in the tables above.<\/p>\n","protected":false},"excerpt":{"rendered":"

Derive the truth table for the following logic gates: a) A 4-input AND gate. b) A 4-input NAND gate. c) A 4-input NOR gate. d) A 4-input XOR gate. e) A 4-input XNOR gate. f) A 5-input XOR gate. g) A 5-input XNOR gate. The correct answer and explanation is : To derive the truth […]<\/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-203050","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/203050","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=203050"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/203050\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=203050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=203050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=203050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}