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 :<\/strong><\/mark><\/p>\n\n\n\n We need to design a digital system that takes a 4-bit binary input and produces a logically low (0) output if the number is a multiple of 3. Otherwise, the output should be logically high (1). However, the output is only valid if the input number is greater than 2.<\/p>\n\n\n\n Since we have a 4-bit binary number, the possible range of inputs is (0000_2) (0) to (1111_2) (15). However, the system\u2019s output is defined only for numbers greater than 2, so the valid range is 3 to 15<\/strong>.<\/p>\n\n\n\n The multiples of 3 within this range are:<\/p>\n\n\n\n For these inputs, the output should be 0<\/strong> (logically low). For all other inputs in the range of 3 to 15, the output should be 1<\/strong> (logically high).<\/p>\n\n\n\n Let ( A, B, C, D ) be the input bits, where ( A ) is the MSB and ( D ) is the LSB. We derive the Boolean function that is low (0) for multiples of 3<\/strong>.<\/p>\n\n\n\n Using Sum of Products (SOP) for when the output is 0: Using a Karnaugh Map (K-map) simplification, the final expression for ( Y ) (Output) will be derived. The simplest logic circuit can be implemented using AND, OR, and NOT gates<\/strong>.<\/p>\n\n\n\n This design helps to determine whether a 4-bit number is a multiple of 3 efficiently using combinational logic.<\/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 : Design of […]<\/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-196810","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196810","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=196810"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196810\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=196810"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=196810"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=196810"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Design of a Digital System to Detect Multiples of 3 (with Defined Output for Inputs Greater than 2)<\/strong><\/h3>\n\n\n\n
Problem Statement<\/strong><\/h4>\n\n\n\n
Step 1: Identifying Valid Inputs<\/strong><\/h4>\n\n\n\n
Step 2: Identifying Multiples of 3<\/strong><\/h4>\n\n\n\n
\n
Step 3: Deriving the Logic Expression<\/strong><\/h4>\n\n\n\n
[
F(A, B, C, D) = \\sum m(3, 6, 9, 12, 15)
]
The complement of this function will give the required output ( Y ), which is high for non-multiples of 3.<\/p>\n\n\n\n