{"id":160490,"date":"2023-09-28T14:10:04","date_gmt":"2023-09-28T08:40:04","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=160490"},"modified":"2023-09-28T14:10:05","modified_gmt":"2023-09-28T08:40:05","slug":"a-function-%f0%9d%90%b9%f0%9d%90%b4-%f0%9d%90%b5-%f0%9d%90%b6-defined-by-three-boolean-variables-a-b-and-c-when-expressed-as-sum-of-products-is-given-by","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-function-%f0%9d%90%b9%f0%9d%90%b4-%f0%9d%90%b5-%f0%9d%90%b6-defined-by-three-boolean-variables-a-b-and-c-when-expressed-as-sum-of-products-is-given-by\/","title":{"rendered":"A function \ud835\udc39(\ud835\udc34, \ud835\udc35, \ud835\udc36) defined by three Boolean variables A, B and C when expressed as sum of products is given by"},"content":{"rendered":"\n<p>Q. A function \ud835\udc39(\ud835\udc34, \ud835\udc35, \ud835\udc36) defined by three Boolean variables <em>A<\/em>, <em>B <\/em>and <em>C <\/em>when expressed as sum of products is given by<\/p>\n\n\n\n<p>\ud835\udc39 = \ud835\udc34\u0305 \u22c5 \ud835\udc35\u0305 \u22c5 \ud835\udc36\u0305 + \ud835\udc34\u0305 \u22c5 \ud835\udc35 \u22c5 \ud835\udc36\u0305 + \ud835\udc34 \u22c5 \ud835\udc35\u0305 \u22c5 \ud835\udc36\u0305<\/p>\n\n\n\n<p>where, \ud835\udc34\u0305, \ud835\udc35\u0305, and \ud835\udc36\u0305 are the complements of the respective variables. The product of sums (POS) form of the function F is<\/p>\n\n\n\n<p>(A) \ud835\udc39 = (\ud835\udc34 + \ud835\udc35 + \ud835\udc36) \u22c5 (\ud835\udc34 + \ud835\udc35\u0305 + \ud835\udc36) \u22c5 (\ud835\udc34\u0305 + \ud835\udc35 + \ud835\udc36)<\/p>\n\n\n\n<p>(B) \ud835\udc39 = (\ud835\udc34\u0305 + \ud835\udc35\u0305 + \ud835\udc36\u0305) \u22c5 (\ud835\udc34\u0305 + \ud835\udc35 + \ud835\udc36\u0305) \u22c5 (\ud835\udc34 + \ud835\udc35\u0305 + \ud835\udc36\u0305)<\/p>\n\n\n\n<p>(C) \ud835\udc39 = (\ud835\udc34 + \ud835\udc35 + \ud835\udc36\u0305) \u22c5 (\ud835\udc34 + \ud835\udc35\u0305 + \ud835\udc36\u0305) \u22c5 (\ud835\udc34\u0305 + \ud835\udc35 + \ud835\udc36\u0305) \u22c5 (\ud835\udc34\u0305 + \ud835\udc35\u0305 + \ud835\udc36) \u22c5 (\ud835\udc34\u0305 + \ud835\udc35\u0305 + \ud835\udc36\u0305)<\/p>\n\n\n\n<p>(D) \ud835\udc39 = (\ud835\udc34\u0305 + \ud835\udc35\u0305 + \ud835\udc36) \u22c5 (\ud835\udc34\u0305 + \ud835\udc35 + \ud835\udc36) \u22c5 (\ud835\udc34 + \ud835\udc35\u0305 + \ud835\udc36) \u22c5 (\ud835\udc34 + \ud835\udc35 + \ud835\udc36\u0305) \u22c5 (\ud835\udc34 + \ud835\udc35 + \ud835\udc36)<\/p>\n\n\n\n<p>Ans: F = (A + B + C\u0305) . (A + B\u0305 + C\u0305) . (A\u0305 + B + C\u0305) . (A\u0305 + B\u0305 + C) . (A\u0305 + B\u0305 + C\u0305)<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>F = A\u0305.B\u0305.C\u0305 + A\u0305.B.C\u0305 + A.B\u0305.C\u0305 <\/p>\n\n\n\n<p>In terms of minterms, this can be represented as: <\/p>\n\n\n\n<p>F = \u2211m\u00a0(0, 2, 4) <\/p>\n\n\n\n<p>The equivalent maxterm will contain the terms not present in the minterm representation, i.e. <\/p>\n\n\n\n<p>F =\u00a0\u2211m (0, 2, 4) = \u03c0(1, 3, 5, 6, 7) = M1. M3. M5. M6. M7 <\/p>\n\n\n\n<p>\u21d2 (A + B + C\u0305) (A + B\u0305 + C\u0305) (A\u0305 + B + C\u0305) (A\u0305 + B\u0305 + C) (A\u0305 + B\u0305 + C\u0305)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. A function \ud835\udc39(\ud835\udc34, \ud835\udc35, \ud835\udc36) defined by three Boolean variables A, B and C when expressed as sum of products is given by \ud835\udc39 = \ud835\udc34\u0305 \u22c5 \ud835\udc35\u0305 \u22c5 \ud835\udc36\u0305 + \ud835\udc34\u0305 \u22c5 \ud835\udc35 \u22c5 \ud835\udc36\u0305 + \ud835\udc34 \u22c5 \ud835\udc35\u0305 \u22c5 \ud835\udc36\u0305 where, \ud835\udc34\u0305, \ud835\udc35\u0305, and \ud835\udc36\u0305 are the complements of the respective variables. [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":160491,"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-160490","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\/160490","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=160490"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160490\/revisions"}],"predecessor-version":[{"id":160492,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160490\/revisions\/160492"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/160491"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=160490"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=160490"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=160490"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}