{"id":154177,"date":"2023-08-03T11:22:26","date_gmt":"2023-08-03T05:52:26","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=154177"},"modified":"2023-08-03T11:22:30","modified_gmt":"2023-08-03T05:52:30","slug":"what-is-the-minimum-number-of-2-input-nor-gates-required-to-implement-a-4-variable-function-expressed-in-sum-of-minterms-form-as-f-%cf%83-0-2-5-7-8-10-13-15","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/what-is-the-minimum-number-of-2-input-nor-gates-required-to-implement-a-4-variable-function-expressed-in-sum-of-minterms-form-as-f-%cf%83-0-2-5-7-8-10-13-15\/","title":{"rendered":"What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of-minterms form as f = \u03a3 (0, 2, 5, 7, 8, 10, 13, 15)?"},"content":{"rendered":"\n<p>Q. What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of-minterms form as f = \u03a3 (0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available. Answer:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 .<\/p>\n\n\n\n<p>Ans:<\/p>\n\n\n\n<p>K-map for given,<\/p>\n\n\n\n<p>f = \u03a3(0, 2, 5, 7, 8, 10, 13, 15)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-494.png\" alt=\"\" class=\"wp-image-154178\" width=\"400\" height=\"268\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-494.png 484w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-494-300x201.png 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/figure>\n\n\n\n<p>Therefore,<\/p>\n\n\n\n<p>f = BD +B&#8217;D&#8217;<\/p>\n\n\n\n<p>= (B&#8217; + D).(B + D&#8217;)<\/p>\n\n\n\n<p>Since all the inputs and their complements are available, so circuit implementation using NOR gate:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-495.png\" alt=\"\" class=\"wp-image-154179\" width=\"410\" height=\"207\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-495.png 618w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-495-300x151.png 300w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/><\/figure>\n\n\n\n<p>F can be implemented using&nbsp;<strong>3<\/strong>&nbsp;NOR gates.<\/p>\n\n\n\n<p>So, option (A) is correct.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of-minterms form as f = \u03a3 (0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available. Answer:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 . Ans: K-map for given, f = \u03a3(0, 2, 5, 7, 8, [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":154180,"comment_status":"open","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-4)","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-4)","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-4)","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":[5141],"tags":[5140],"class_list":["post-154177","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154177","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=154177"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154177\/revisions"}],"predecessor-version":[{"id":154181,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154177\/revisions\/154181"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/154180"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=154177"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=154177"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=154177"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}