{"id":4466,"date":"2025-03-10T16:56:34","date_gmt":"2025-03-10T11:26:34","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=4466"},"modified":"2025-07-16T14:18:49","modified_gmt":"2025-07-16T08:48:49","slug":"karnaugh-map","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ee\/boolean-algebra\/karnaugh-map","title":{"rendered":"Karnaugh Map"},"content":{"rendered":"<p style=\"text-align: justify;\">The \u201c<strong>Karnaugh map<\/strong>\u201d is a graphical method which provides a systematic method for simplifying and manipulating the Boolean expressions or to convert a truth table to its corresponding logic circuit in a simple, orderly process.<\/p>\n<p style=\"text-align: justify;\">In this technique, the information contained in a truth table or available in SOP or POS form is represented on a K-map.<\/p>\n<p style=\"text-align: justify;\">Although this technique may be used for any number of variables, it is generally used up to 6 variables, beyond which it becomes very cumbersome.<\/p>\n<p style=\"text-align: justify;\">In n-variable K-map there are 2n cells.<\/p>\n<p style=\"text-align: justify;\">\u201cGray code\u201d has been used for the identification of cells.<\/p>\n<h3 style=\"text-align: justify;\">\u00a0Three-variable K-map<\/h3>\n<ul style=\"text-align: justify;\">\n<li>Four cells<\/li>\n<li>Four minterms (maxterms)<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4467 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/03\/maxterms.jpg\" alt=\"Maxterms\" width=\"448\" height=\"159\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/maxterms.jpg 448w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/maxterms-300x106.jpg 300w\" sizes=\"auto, (max-width: 448px) 100vw, 448px\" \/><\/p>\n<h3 style=\"text-align: justify;\">Three-variable K-map<\/h3>\n<ul style=\"text-align: justify;\">\n<li>Eight cells<\/li>\n<li>Eight minterms (maxterms)<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4468 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/03\/three-variable-k-map.png\" alt=\" Three-variable K-map\" width=\"500\" height=\"147\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/three-variable-k-map.png 500w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/three-variable-k-map-300x88.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/p>\n<h3 style=\"text-align: justify;\">Four-variable K-map<\/h3>\n<ul style=\"text-align: justify;\">\n<li>Sixteen cells<\/li>\n<li>Sixteen minterms (maxterms)<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4469 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/03\/four-variable-k-map.jpg\" alt=\" Four-variable K-map \" width=\"572\" height=\"217\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/four-variable-k-map.jpg 572w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/four-variable-k-map-300x114.jpg 300w\" sizes=\"auto, (max-width: 572px) 100vw, 572px\" \/><\/p>\n<h3 style=\"text-align: justify;\">Implicant<\/h3>\n<p style=\"text-align: justify;\">Implicant is a product\/sum term in sum of product (SOP) for which the function output must be 1 or sum\/maxterm term in product of sum (POS) of a boolean function.<\/p>\n<h3 style=\"text-align: justify;\">Prime Implicant<\/h3>\n<p style=\"text-align: justify;\">A prime Implicant is a smallest possible sum\/product term of the given function, removing any one of the literal from which is not possible. All possible groups formed in K-map are prime implicants.<\/p>\n<p style=\"text-align: justify;\"><strong>Example:<\/strong> Number of prime implicants = 3<\/p>\n<h4 style=\"text-align: justify;\">Essential Prime Implicant (EPI)<\/h4>\n<ul style=\"text-align: justify;\">\n<li>Essential Prime Implicant are those prime implicants which cover atleast one minterm in SOP or atleast one maxterm in POS that can\u2019t be covered by any other prime implicant.<\/li>\n<li>Essential Prime Implicants (EPI) are those prime implicants which always appear in final solution.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong> Example:<\/strong> Number of Essential Prime Implicants (EPI) = 2.<\/p>\n<h4 style=\"text-align: justify;\">Redundant Prime Implicants (RPI)<\/h4>\n<ul style=\"text-align: justify;\">\n<li>The prime implicants for which each of its minterm\/maxterm is covered by some essential prime implicants are redundant prime implicants (RPI).<\/li>\n<li>Redundant Prime Implicants (RPI) never appears in final solution.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong> Example: <\/strong>Redundant Prime Implicant (RPI) = BC<\/p>\n<h4 style=\"text-align: justify;\">Selective Prime Implicants (SPI)<\/h4>\n<p style=\"text-align: justify;\">The prime implicants which are neither essential nor redundant prime implicants are called selective prime implicants. These are also known as non-essential prime implicants.<br \/>\nThey may or may not appear in final solution.<\/p>\n<p style=\"text-align: justify;\"><strong> Example:<\/strong> Number of selective prime implicants = 2.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4473 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/03\/implicant.jpg\" alt=\"Implicant\" width=\"431\" height=\"349\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/implicant.jpg 431w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/implicant-300x243.jpg 300w\" sizes=\"auto, (max-width: 431px) 100vw, 431px\" \/><\/p>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ee\/boolean-algebra\/boolean-algebraic-theorem\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ee\/boolean-algebra\/logic-gates\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-boolean-algebra\" target=\"_blank\" rel=\"noopener\"><strong>What is Boolean algebra?<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The \u201cKarnaugh map\u201d is a graphical method which provides a systematic method for simplifying and manipulating the Boolean expressions or<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1291,5],"tags":[1439,1432,1442,1307,1309,1438,1437,1441,1440,1308,1310],"class_list":["post-4466","post","type-post","status-publish","format-standard","hentry","category-boolean-algebra","category-ee","tag-boolean-simplification","tag-digital-electronics","tag-ee-concepts","tag-four-variable-k-map","tag-implicant","tag-k-map","tag-karnaugh-map","tag-logic-design","tag-logic-minimization","tag-prime-implicant","tag-truth-table"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/4466","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=4466"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/4466\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=4466"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=4466"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=4466"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}