{"id":1565,"date":"2025-01-01T05:58:25","date_gmt":"2024-12-31T22:58:25","guid":{"rendered":"https:\/\/www.tneutron.net\/industri\/?p=1565"},"modified":"2024-12-30T08:34:54","modified_gmt":"2024-12-30T01:34:54","slug":"method-quine-mc-cluskey","status":"publish","type":"post","link":"https:\/\/www.tneutron.net\/industri\/method-quine-mc-cluskey\/","title":{"rendered":"Method Quine &#8211; Mc. Cluskey"},"content":{"rendered":"<p><span class=\"notranslate\">To simplify the logic equations of four variables, Kmap is the most effective method.<\/span> <span class=\"notranslate\"> But if the equation was more than four variables this method will have trouble.<\/span> <span class=\"notranslate\"> Method Quine Mc.<\/span> <span class=\"notranslate\"> Cluskey adalh one possible way to simplify a logical expression of more than four variables.<\/span> <span class=\"notranslate\"> Here are the steps;<\/span><br \/>\n<span class=\"notranslate\"> When given the logic equation F = \u03a3 (0,3,7,8,9,13)<\/span><br \/>\n<span class=\"notranslate\"> a.<\/span> <span class=\"notranslate\"> Declare each element minterm into a binary code<\/span><br \/>\n<span class=\"notranslate\"> 0 = 0000<\/span><br \/>\n<span class=\"notranslate\"> 3 = 0011<\/span><br \/>\n<span class=\"notranslate\"> 7 = 0111<\/span><br \/>\n<span class=\"notranslate\"> 8 = 1000<\/span><br \/>\n<span class=\"notranslate\"> 9 = 1001<\/span><br \/>\n<span class=\"notranslate\"> 13 = 1011<\/span><\/p>\n<p><span class=\"notranslate\"> b.<\/span> <span class=\"notranslate\"> Determine the number of logic 1 in a binary number as an index of numbers.<\/span> <span class=\"notranslate\"> Collect all indexed binary digits together into one group in Table 1<\/span><br \/>\n<span class=\"notranslate\"> 0 = 0000 \u2192 number of logic 1 = 0<\/span><br \/>\n<span class=\"notranslate\"> 3 = 0011 \u2192 number of logic 1 = 2<\/span><br \/>\n<span class=\"notranslate\"> 7 = 0111 \u2192 number of logic 1 = 3<\/span><br \/>\n<span class=\"notranslate\"> 8 = 1000 \u2192 number of logic 1 = 1<\/span><br \/>\n<span class=\"notranslate\"> 9 = 1001 \u2192 number of logic 1 = 2<\/span><br \/>\n<span class=\"notranslate\"> 13 = 1011 \u2192 number of logic 1 = 3<\/span><br \/>\n<a href=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image-7.png\"><img loading=\"lazy\" decoding=\"async\" title=\"image\" src=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image_thumb-8.png\" alt=\"image\" width=\"100\" height=\"141\" border=\"0\" \/><\/a><\/p>\n<p><span class=\"notranslate\"> c.<\/span> <span class=\"notranslate\"> Compare between each element ranging from the smallest index with each element of the index thereafter.<\/span> <span class=\"notranslate\"> The first element of the index value must be less than the value of the index element afterwards.<\/span> <span class=\"notranslate\"> If there is a difference 2n then be merged.<\/span> <span class=\"notranslate\"> This step will generate a new group.<\/span><br \/>\n<span class=\"notranslate\"> d.<\/span> <span class=\"notranslate\"> Make a back step c until there is no difference 2n.<\/span><br \/>\n<span class=\"notranslate\"> e.<\/span> <span class=\"notranslate\"> Each group is given a name.<\/span><br \/>\n<a href=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image-11.png\"><img loading=\"lazy\" decoding=\"async\" title=\"image\" src=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image_thumb-11.png\" alt=\"image\" width=\"473\" height=\"123\" border=\"0\" \/><\/a><\/p>\n<p><span class=\"notranslate\"> f.<\/span> <span class=\"notranslate\"> For completion, we take one name that represents each number (a, b, c or d).<\/span> <span class=\"notranslate\"> Taking the name should be as minimal as possible.<\/span> <span class=\"notranslate\"> So that would be obtained<\/span><br \/>\n<span class=\"notranslate\"> F = a + c + d<\/span><br \/>\n<a href=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image-12.png\"><img loading=\"lazy\" decoding=\"async\" title=\"image\" src=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image_thumb-13.png\" alt=\"image\" width=\"203\" height=\"131\" border=\"0\" \/><\/a><\/p>\n<p><span class=\"notranslate\"> As a simplified example of the logic equations in the truth table below.<\/span><br \/>\n<a href=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image-14.png\"><img loading=\"lazy\" decoding=\"async\" title=\"image\" src=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image_thumb-14.png\" alt=\"image\" width=\"388\" height=\"190\" border=\"0\" \/><\/a><\/p>\n<p><span class=\"notranslate\"> Then the logic circuit<\/span><br \/>\n<a href=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image-15.png\"><img loading=\"lazy\" decoding=\"async\" title=\"image\" src=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image_thumb-15.png\" alt=\"image\" width=\"328\" height=\"259\" border=\"0\" \/><\/a><\/p>\n<p><span class=\"notranslate\"> The above equation can be simplified to the methods described above.<\/span><br \/>\n<span class=\"notranslate\"> <strong>o With Boolean algebra<\/strong><\/span><br \/>\n<a href=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image-16.png\"><img loading=\"lazy\" decoding=\"async\" title=\"image\" src=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image_thumb-16.png\" alt=\"image\" width=\"298\" height=\"123\" border=\"0\" \/><\/a><\/p>\n<p><span class=\"notranslate\"><strong>o With the K-map<\/strong><\/span><br \/>\n<a href=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image-18.png\"><img loading=\"lazy\" decoding=\"async\" title=\"image\" src=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image_thumb-17.png\" alt=\"image\" width=\"297\" height=\"193\" border=\"0\" \/><\/a><\/p>\n<p><span class=\"notranslate\"> <strong>o With venn diagram<\/strong><\/span><br \/>\n<a href=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image-19.png\"><img loading=\"lazy\" decoding=\"async\" title=\"image\" src=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image_thumb-18.png\" alt=\"image\" width=\"287\" height=\"35\" border=\"0\" \/><\/a><\/p>\n<p><a href=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image-21.png\"><img loading=\"lazy\" decoding=\"async\" title=\"image\" src=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image_thumb-20.png\" alt=\"image\" width=\"244\" height=\"181\" border=\"0\" \/><\/a><\/p>\n<p><span class=\"notranslate\"> From the picture beside we can see a circle filled by shading while circle C is not filled by shading only partially filled and the rose is represented by a circle A. so<\/span><br \/>\n<a href=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image-22.png\"><img loading=\"lazy\" decoding=\"async\" title=\"image\" src=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image_thumb-21.png\" alt=\"image\" width=\"85\" height=\"41\" border=\"0\" \/><\/a><\/p>\n<p><span class=\"notranslate\"> <strong>o With Quine Mc-Cluskey<\/strong><\/span><br \/>\n<a href=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image-23.png\"><img loading=\"lazy\" decoding=\"async\" title=\"image\" src=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image_thumb-22.png\" alt=\"image\" width=\"388\" height=\"287\" border=\"0\" \/><\/a><\/p>\n<p><a href=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image-24.png\"><img loading=\"lazy\" decoding=\"async\" title=\"image\" src=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image_thumb-24.png\" alt=\"image\" width=\"308\" height=\"81\" border=\"0\" \/><\/a><br \/>\n<span class=\"notranslate\"> F = a + b \u2192 (0,2,4,6) + (4,5,6,7)<\/span><br \/>\n<a href=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image-28.png\"><img loading=\"lazy\" decoding=\"async\" title=\"image\" src=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image_thumb-28.png\" alt=\"image\" width=\"244\" height=\"190\" border=\"0\" \/><\/a><\/p>\n<p><span class=\"notranslate\">So simplification unpleasent above logic can be implemented in sequence as follows;<\/span><br \/>\n<a href=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image-30.png\"><img loading=\"lazy\" decoding=\"async\" title=\"image\" src=\"https:\/\/www.tneutron.net\/industri\/wp-content\/uploads\/sites\/3\/2016\/11\/image_thumb-29.png\" alt=\"image\" width=\"302\" height=\"122\" border=\"0\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>To simplify the logic equations of four variables, Kmap is the most effective method. But if the equation was more<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"colormag_page_container_layout":"default_layout","colormag_page_sidebar_layout":"default_layout","footnotes":""},"categories":[1830],"tags":[1921,1923,1918,1919,1920,1922,1926,1924,1925],"class_list":["post-1565","post","type-post","status-publish","format-standard","hentry","category-english","tag-metodu0105-quine-a-mccluskeya","tag-metoda-lui-quine","tag-metoda-quine","tag-metoda-quine-mc-cluskey","tag-metoda-quineu0027a-mccluskeya-przyku0142ad","tag-metoda-quineu0027a-mccluskeya-przyku0142ady","tag-metoda-quinea","tag-minimalizacja-funkcji-metodu0105-quineu0027a-mccluskeya","tag-minimalizacja-metodu0105-quineu0027a"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Method Quine - Mc. 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