{"id":320,"date":"2020-04-06T10:49:53","date_gmt":"2020-04-06T10:49:53","guid":{"rendered":"http:\/\/ekomartantoh.net\/artikel\/?p=320"},"modified":"2020-05-10T15:27:14","modified_gmt":"2020-05-10T15:27:14","slug":"metode-penyederhanaan-rangkaian-logika","status":"publish","type":"post","link":"https:\/\/ekomartantoh.net\/artikel\/2020\/04\/06\/metode-penyederhanaan-rangkaian-logika\/","title":{"rendered":"Metode Penyederhanaan Rangkaian Logika"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Sum of Product Form<\/h2>\n\n\n\n<p>Metode penyederhanaan rangkaian logika salah satunya adalah SOP (Sum of Product)<\/p>\n\n\n\n<p>Contoh:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-2.png\" alt=\"Contoh Sum of Product\" class=\"wp-image-321\" width=\"246\" height=\"73\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-2.png 363w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-2-300x88.png 300w\" sizes=\"auto, (max-width: 246px) 100vw, 246px\" \/><\/figure>\n\n\n\n<p>Setiap pernyataan dalam bentuk sum of products terdiri dari dua atau lebih operasi AND yang semuanya di OR kan.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Product of Sum<\/h2>\n\n\n\n<p>Bentuk persamaan logika juga menggunakan POS (Products of Sum). Teridiri dari 2 atau lebih operasi OR  yang kemudian di AND kan.<\/p>\n\n\n\n<p>Contoh:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-3.png\" alt=\"Contoh Products of Sum\" class=\"wp-image-322\" width=\"343\" height=\"81\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-3.png 449w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-3-300x71.png 300w\" sizes=\"auto, (max-width: 343px) 100vw, 343px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Algegraic Simplification<\/h2>\n\n\n\n<p>Sebuah pernyataan boolean dapat kita sederhanakan bentuknya dengan menggunakan banyak cara, pernyataan yang baru digunakan untuk mengimplementasikan sebuah rangkaian yang sama dengan rangkaian asli, tetapi memiliki gerbang dan koneksi yang lebih sedikit.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"626\" height=\"305\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-4.png\" alt=\"Contoh penyederhanaan persamaan logika\" class=\"wp-image-323\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-4.png 626w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-4-300x146.png 300w\" sizes=\"auto, (max-width: 626px) 100vw, 626px\" \/><\/figure>\n\n\n\n<p>Contoh:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"696\" height=\"304\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-6.png\" alt=\"Penyederhanaan Rangkaian Logika\" class=\"wp-image-326\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-6.png 696w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-6-300x131.png 300w\" sizes=\"auto, (max-width: 696px) 100vw, 696px\" \/><\/figure>\n\n\n\n<p>Langkah-langkah:<\/p>\n\n\n\n<p>Menggunakan teori demorgan &#8211; &gt; Menghasilkan SOP<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"560\" height=\"370\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-7.png\" alt=\"Store of Products\" class=\"wp-image-328\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-7.png 560w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-7-300x198.png 300w\" sizes=\"auto, (max-width: 560px) 100vw, 560px\" \/><\/figure>\n\n\n\n<p>Rangkaian sederhana:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"571\" height=\"104\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-8.png\" alt=\"\" class=\"wp-image-329\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-8.png 571w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-8-300x55.png 300w\" sizes=\"auto, (max-width: 571px) 100vw, 571px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Complete Design Procedure <\/h2>\n\n\n\n<p>Setiap masalah logika dapat diselesaikan dengan langkah-langkah sebagai berikut:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Interpret the problem and set up a truth table to describe its operation. <\/li><li>Write the AND (product) term for each case where the output is 1.<\/li><li>Write the sum-of-products (SOP) expression for the output.<\/li><li>Simplify the output expression if possible.<\/li><li>Implement the circuit for the final, simplified expression.<\/li><\/ol>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>Contoh :<br>Rancanglah sebuah rangkaian logika yang memiliki 3 input A, B dan C, dimana output akan menjadi HIGH hanya pada saat semua input mayoritas adalah HIGH.<\/p>\n\n\n\n<p>Solusi<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Menterjemahkan masalah dan membuat table kebenaran<\/li><\/ol>\n\n\n\n<p>Output = 1 apabila mayoritas input adalah 1 (2\/lebih input), dan yang lain output = 0<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"187\" height=\"266\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-9.png\" alt=\"Penyederhanaan Rangkaian Logika\" class=\"wp-image-333\"\/><\/figure>\n\n\n\n<p>2. Membuat persamaan AND untuk output = 1<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"253\" height=\"258\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-10.png\" alt=\"Penyederhanaan Persamaan Logika\" class=\"wp-image-334\"\/><\/figure>\n\n\n\n<p>3. Menulis persamaan sum of products untuk output<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"323\" height=\"37\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-11.png\" alt=\"\" class=\"wp-image-335\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-11.png 323w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-11-300x34.png 300w\" sizes=\"auto, (max-width: 323px) 100vw, 323px\" \/><\/figure>\n\n\n\n<p>4. Menyederhanakan persamaan<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"471\" height=\"126\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-12.png\" alt=\"Menyederhakan Persamaan Logika\" class=\"wp-image-337\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-12.png 471w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-12-300x80.png 300w\" sizes=\"auto, (max-width: 471px) 100vw, 471px\" \/><\/figure>\n\n\n\n<p>5. Implementasi rangkaian untuk persamaan terakhir<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"491\" height=\"246\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-13.png\" alt=\"Menyederhanakan Rangkaian Logika\" class=\"wp-image-338\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-13.png 491w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-13-300x150.png 300w\" sizes=\"auto, (max-width: 491px) 100vw, 491px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Karnough Map Method<\/h2>\n\n\n\n<p>Karnaugh Map (K-Map) merupakan tool grafis yang digunakan untuk menyederhakan persamaan logika atau untuk melakukan konversi sebuah tabel kebenaran menjadi rangkaian logika yang lebih sederhana.<\/p>\n\n\n\n<p>Contoh:<\/p>\n\n\n\n<p>Peta Karnaugh 2 variabel<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"635\" height=\"142\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-14.png\" alt=\"Peta karnaugh 2 variabel\" class=\"wp-image-340\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-14.png 635w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-14-300x67.png 300w\" sizes=\"auto, (max-width: 635px) 100vw, 635px\" \/><\/figure>\n\n\n\n<p>Peta Karnaugh 3 variabel<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"632\" height=\"250\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-15.png\" alt=\"Peta Karnaugh\" class=\"wp-image-341\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-15.png 632w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-15-300x119.png 300w\" sizes=\"auto, (max-width: 632px) 100vw, 632px\" \/><\/figure>\n\n\n\n<p>Peta Karnaugh 4 variabel<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"690\" height=\"376\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-23.png\" alt=\"4 variabel\" class=\"wp-image-351\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-23.png 690w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-23-300x163.png 300w\" sizes=\"auto, (max-width: 690px) 100vw, 690px\" \/><\/figure>\n\n\n\n<p>Persamaaan output x dapat disederhanakan dengan cara membuat kotak pada Kmap untuk yang berisi 1. Porses ini disebut <strong>looping<\/strong>.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Looping -&gt; 2<\/h4>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"687\" height=\"571\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-17.png\" alt=\"looping 2\" class=\"wp-image-343\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-17.png 687w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-17-300x249.png 300w\" sizes=\"auto, (max-width: 687px) 100vw, 687px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Looping -&gt; 4<\/h4>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"682\" height=\"254\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-18.png\" alt=\"looping 4\" class=\"wp-image-344\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-18.png 682w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-18-300x112.png 300w\" sizes=\"auto, (max-width: 682px) 100vw, 682px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"633\" height=\"290\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-19.png\" alt=\"looping 4\" class=\"wp-image-345\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-19.png 633w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-19-300x137.png 300w\" sizes=\"auto, (max-width: 633px) 100vw, 633px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Looping -&gt; 8<\/h4>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"576\" height=\"639\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-20.png\" alt=\"Looping 8\" class=\"wp-image-346\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-20.png 576w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-20-270x300.png 270w\" sizes=\"auto, (max-width: 576px) 100vw, 576px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Prosedur Penyederhanaan<\/h4>\n\n\n\n<ul class=\"wp-block-list\"><li>Step 1 Construct the K map and place 1s in those squares corresponding to the 1s in the truth table. Place 0s in the other squares.<\/li><li>Step 2 Examine the map for adjacent 1s and loop those 1s that are not adjacent to any other 1s. These are called isolated 1s.<\/li><li>Step 3 Next, look for those 1s that are adjacent to only one other 1. Loop any pair containing such a 1.<\/li><li>Step 4 Loop any octet even if it contains some 1s that have already been looped.<\/li><li>Step 5 Loop any quad that contains one or more 1s that have not already been looped, making sure to use the minimum number of loops.<\/li><li>Step 6 Loop any pairs necessary to include any 1s that have not yet been looped, making sure to use the minimum number of loops.<\/li><li>Step 7 Form the OR sum of all the terms generated by each loop.<\/li><\/ul>\n\n\n\n<p>Contoh:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"616\" height=\"543\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-21.png\" alt=\"Prosedure penyederhanaan\" class=\"wp-image-348\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-21.png 616w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-21-300x264.png 300w\" sizes=\"auto, (max-width: 616px) 100vw, 616px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"610\" height=\"275\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-22.png\" alt=\"Karnaugh Map\" class=\"wp-image-349\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-22.png 610w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/04\/image-22-300x135.png 300w\" sizes=\"auto, (max-width: 610px) 100vw, 610px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Sistem Digital - Sesi 6 - Kelas Pagi\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/TwJ4QkBrH0I?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><figcaption>Recording kelas Pagi<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Sistem Digital - Sesi 6 - Kelas Malam\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/FcuKvzSgt9M?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><figcaption>Recording Kelas Malam<\/figcaption><\/figure>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sum of Product Form Metode penyederhanaan rangkaian logika salah satunya adalah SOP (Sum of Product) Contoh: Setiap pernyataan dalam bentuk sum of products terdiri dari dua atau lebih operasi AND yang semuanya di OR kan. Product of Sum Bentuk persamaan logika juga menggunakan POS (Products of Sum). Teridiri dari 2 atau lebih operasi OR yang [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[35],"tags":[],"class_list":["post-320","post","type-post","status-publish","format-standard","hentry","category-sistem-digital"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Metode Penyederhanaan Rangkaian Logika - eko&#039;s Article<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ekomartantoh.net\/artikel\/2020\/04\/06\/metode-penyederhanaan-rangkaian-logika\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Metode Penyederhanaan Rangkaian Logika - eko&#039;s Article\" \/>\n<meta property=\"og:description\" content=\"Sum of Product Form Metode penyederhanaan rangkaian logika salah satunya adalah SOP (Sum of Product) Contoh: Setiap pernyataan dalam bentuk sum of products terdiri dari dua atau lebih operasi AND yang semuanya di OR kan. 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