Design a digital system whose output is defined as logically low. If the 4 bit inpur binary number is a multiple of 3. Otherwise, the output will be logically high. The output is defined if and only if the input binary number is greater than 2<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To design the digital system, we define the output We can implement this with combinational logic using a 4-bit input and a truth table to drive the output logic.<\/p>\n\n\n\n This digital system requires a combinational logic circuit with a 4-bit binary input and a single binary output. The core function of the system is to determine whether a binary input value meets specific conditions and set the output accordingly.<\/p>\n\n\n\n The input is a 4-bit binary number, meaning it can represent values from 0 to 15 (decimal). The system should only define the output if the input value is greater than 2<\/strong>. Therefore, values 0, 1, and 2 are considered undefined<\/strong> and need not be processed in the logic.<\/p>\n\n\n\n The system must recognize if the valid input (greater than 2) is a multiple of 3. In the decimal range of 3 to 15, the multiples of 3 are: If the input matches one of these values, the output To implement this in digital logic:<\/p>\n\n\n\n Alternatively, a ROM-based solution<\/strong> or PLD (Programmable Logic Device)<\/strong> can use a lookup table matching the truth table above. This approach is efficient when dealing with small input spaces like a 4-bit system.<\/p>\n\n\n\n This digital logic system is useful for control applications where actions depend on numeric thresholds and specific divisibility. Designing the output based on arithmetic properties like “greater than” and “multiple of” allows for sophisticated decision-making in digital electronics.<\/p>\n","protected":false},"excerpt":{"rendered":" Design a digital system whose output is defined as logically low. If the 4 bit inpur binary number is a multiple of 3. Otherwise, the output will be logically high. The output is defined if and only if the input binary number is greater than 2 The Correct Answer and Explanation is: Correct Answer: To […]<\/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-217052","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217052","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=217052"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217052\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=217052"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=217052"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=217052"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Correct Answer:<\/h3>\n\n\n\n
Y<\/code> as follows:<\/p>\n\n\n\n\n
A = A3A2A1A0<\/code> (where A3 is MSB, A0 is LSB) represents a number greater than 2 AND<\/strong> is a multiple of 3 \u2192 Output Y = 0<\/code> (LOGICALLY LOW).<\/li>\n\n\n\nY = 1<\/code> (LOGICALLY HIGH).<\/li>\n\n\n\n
\n\n\n\nTruth Table:<\/h3>\n\n\n\n
Decimal<\/th> Binary<\/th> >2?<\/th> Mod 3 = 0?<\/th> Output Y<\/th><\/tr><\/thead> 0<\/td> 0000<\/td> No<\/td> Yes<\/td> X (undef)<\/td><\/tr> 1<\/td> 0001<\/td> No<\/td> No<\/td> X (undef)<\/td><\/tr> 2<\/td> 0010<\/td> No<\/td> No<\/td> X (undef)<\/td><\/tr> 3<\/td> 0011<\/td> Yes<\/td> Yes<\/td> 0<\/td><\/tr> 4<\/td> 0100<\/td> Yes<\/td> No<\/td> 1<\/td><\/tr> 5<\/td> 0101<\/td> Yes<\/td> No<\/td> 1<\/td><\/tr> 6<\/td> 0110<\/td> Yes<\/td> Yes<\/td> 0<\/td><\/tr> 7<\/td> 0111<\/td> Yes<\/td> No<\/td> 1<\/td><\/tr> 8<\/td> 1000<\/td> Yes<\/td> No<\/td> 1<\/td><\/tr> 9<\/td> 1001<\/td> Yes<\/td> Yes<\/td> 0<\/td><\/tr> 10<\/td> 1010<\/td> Yes<\/td> No<\/td> 1<\/td><\/tr> 11<\/td> 1011<\/td> Yes<\/td> No<\/td> 1<\/td><\/tr> 12<\/td> 1100<\/td> Yes<\/td> Yes<\/td> 0<\/td><\/tr> 13<\/td> 1101<\/td> Yes<\/td> No<\/td> 1<\/td><\/tr> 14<\/td> 1110<\/td> Yes<\/td> No<\/td> 1<\/td><\/tr> 15<\/td> 1111<\/td> Yes<\/td> No<\/td> 1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\nExplanation (300+ words):<\/h3>\n\n\n\n
1. Understanding the Input Conditions:<\/strong><\/h4>\n\n\n\n
2. Multiples of 3:<\/strong><\/h4>\n\n\n\n
3, 6, 9, and 12<\/strong>.<\/p>\n\n\n\nY<\/code> must be logically LOW (0)<\/strong>. For all other defined values (greater than 2 but not divisible by 3), the output should be logically HIGH (1)<\/strong>.<\/p>\n\n\n\n3. Digital Implementation:<\/strong><\/h4>\n\n\n\n
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Conclusion:<\/strong><\/h4>\n\n\n\n