Q. Consider the minterm list form of a Boolean function \ud835\udc39 given below.<\/p>\n\n\n\n
\ud835\udc39(\ud835\udc43, \ud835\udc44, \ud835\udc45, \ud835\udc46) = \u2211 \ud835\udc5a(0, 2, 5, 7, 9, 11) + \ud835\udc51(3, 8, 10, 12, 14)<\/p>\n\n\n\n
Here, \ud835\udc5a denotes a minterm and \ud835\udc51 denotes a don\u2019t care term. The number of essential prime implicants of the function \ud835\udc39 is_______.<\/p>\n\n\n\n
Ans: 3<\/p>\n\n\n\n
Sol:<\/p>\n\n\n\n
Essential Prime Implicants\u00a0are those subcubes (groups) which cover atleast one minterm that can\u2019t be covered by any other prime implicant. Essential prime implicants (EPI) are those prime implicants which always appear in final solution.<\/p>\n\n\n\n
There are three prime implicants P\u2019QS, PQ\u2019 and Q\u2019S\u2019. Also, all of them are essential. Therefore, the number of essential prime implicants of function F is\u00a03<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" Q. Consider the minterm list form of a Boolean function \ud835\udc39 given below. \ud835\udc39(\ud835\udc43, \ud835\udc44, \ud835\udc45, \ud835\udc46) = \u2211 \ud835\udc5a(0, 2, 5, 7, 9, 11) + \ud835\udc51(3, 8, 10, 12, 14) Here, \ud835\udc5a denotes a minterm and \ud835\udc51 denotes a don\u2019t care term. The number of essential prime implicants of the function \ud835\udc39 is_______. Ans: […]<\/p>\n","protected":false},"author":419,"featured_media":160361,"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-160360","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\/160360","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=160360"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160360\/revisions"}],"predecessor-version":[{"id":160362,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160360\/revisions\/160362"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/160361"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=160360"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=160360"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=160360"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}