{"id":155,"date":"2020-02-23T14:03:07","date_gmt":"2020-02-23T14:03:07","guid":{"rendered":"http:\/\/ekomartantoh.net\/artikel\/?p=155"},"modified":"2020-02-23T14:06:57","modified_gmt":"2020-02-23T14:06:57","slug":"operasi-bilangan-biner-dan-koplemen","status":"publish","type":"post","link":"https:\/\/ekomartantoh.net\/artikel\/2020\/02\/23\/operasi-bilangan-biner-dan-koplemen\/","title":{"rendered":"Operasi Bilangan Biner dan Komplemen"},"content":{"rendered":"\n<p>Operasi bilangan biner akan membahas beberapa point seperti operasi penjumlahan bilangan biner, perkalian bilangan biner dan pembagian bilangan biner.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Operasi Bilangan Biner &#8211; Penjumlahan<\/h2>\n\n\n\n<p>Ada beberapa hal umum yang harus diketahui dalam penjumlahan bilangan biner yaitu sebagai berikut:<\/p>\n\n\n\n<p>0 + 0 = 0<\/p>\n\n\n\n<p>0 + 1 = 1<\/p>\n\n\n\n<p>1 + 0 = 1<\/p>\n\n\n\n<p>1 + 1 = 10 -> 0 + carry 1 ditempatkan pada posisi berikutnya<\/p>\n\n\n\n<p>1 + 1 + 1 = 11 -> 1 + carry 1 ditempatkan pada posisi berikutnya<\/p>\n\n\n\n<p>contoh penjumlahan dalam bilangan biner:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"738\" height=\"133\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-12.png\" alt=\"Penjumlahan bilangan biner\" class=\"wp-image-156\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-12.png 738w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-12-300x54.png 300w\" sizes=\"auto, (max-width: 738px) 100vw, 738px\" \/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Bilangan Bertanda<\/h2>\n\n\n\n<p>Sebagian besar komputer digital menangani bilangan negatif sebagai bilangan positif, sehingga diperlukan sign (tanda) bilangan + atau -.Tanda tersebut diwakili oleh satu bit yang disebut sign bit. Dimana 0 merupakan tanda positif dan 1 merupakan tanda negatif. Bit tanda ini menempati posisi bit paling kiri atau pada bagian MSB.<\/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\/02\/image-13.png\" alt=\"Bilangan Bertanda\" class=\"wp-image-157\" width=\"485\" height=\"322\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-13.png 618w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-13-300x200.png 300w\" sizes=\"auto, (max-width: 485px) 100vw, 485px\" \/><\/figure>\n\n\n\n<p>Sign bit digunakan untuk menyatakan bilangan positif dan negatif yang disimpan dalam bentuk bilangan biner. Terilahat pada gambar bahwa bilangan tersebut terdiri dari 1 sign bit dan 6 magnitude bit. Magnitude bit merupakan bilangan biner yang nilainya sama dengan bilangan desimal yang mewakilinya. Prinsip ini dikenal dengan nama <strong>sign magnitude system<\/strong> untuk menyatakan bilangan biner bertanda.<\/p>\n\n\n\n<p>System yang umum digunakan untuk menyatakan biangan biner bertanda ini 2&#8217;s complement system. Komplemen 2 ini digunakan untuk menyatakan bilangan bertanda, karena untuk melakukan operasi pengurangan, sebenarnya operasi yang dilakukan adalah penjumlahan.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Langkah-langkah Melakukan Komplemen 2:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\"> 1&#8217;s-Complement Form <\/h4>\n\n\n\n<p>Komplemen 1 dari sebuah bilangan biner merupakan diperoleh dari perubahan 0 menjadi 1, dan 1 menjadi 0.<\/p>\n\n\n\n<p>contoh:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"748\" height=\"108\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-14.png\" alt=\"Komplemen 1\" class=\"wp-image-159\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-14.png 748w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-14-300x43.png 300w\" sizes=\"auto, (max-width: 748px) 100vw, 748px\" \/><\/figure>\n\n\n\n<p>Komplemen 1 dari 101101 adalah 010010<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2&#8217;s-Complement Form<\/h4>\n\n\n\n<p>Komplemen 2 dari sebuah bilangan biner diperoleh dari hasil komplemen 1 ditambah dengan 1 pada posisi LSB<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"811\" height=\"149\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-15.png\" alt=\"Komplement 2\" class=\"wp-image-160\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-15.png 811w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-15-300x55.png 300w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-15-768x141.png 768w\" sizes=\"auto, (max-width: 811px) 100vw, 811px\" \/><\/figure>\n\n\n\n<p>Sehingga 010011 merupakan komplemen 2 dari 101101<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Representing Signed Nember Using 2&#8217;s Complement<\/h4>\n\n\n\n<p>Sistem komplemen 2 digunakan untuk menyatakan bilangan bertanda.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Jika bilangan positif, magnitude dinyatakan dalam bentuk bilangan biner asli dengan sign bit adalah 0 ditempatkan pada bagian MSB.<\/li><li>Jika bilangan negatif, maka magnitude merupakan bentuk komplemen 2, dan sign bit 1 ditempatkan pada bagian MSB.<\/li><\/ul>\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\/02\/image-16.png\" alt=\"Bilangan bertanda dengan komplemen 2\" class=\"wp-image-162\" width=\"467\" height=\"260\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-16.png 629w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-16-300x167.png 300w\" sizes=\"auto, (max-width: 467px) 100vw, 467px\" \/><figcaption>Bilangan Bertanda dengan Koplemen 2<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Penjumlahan Komplemen 2<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Case1: Two Positif Number<\/h4>\n\n\n\n<p>Menjumlahkan 2 bilangan positif sama seperti penjumlahan bilangan biner diatas. Contoh: +9 dan +4<\/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\/02\/image-17.png\" alt=\"Penjumlahan 2 bilangan Positif\" class=\"wp-image-163\" width=\"262\" height=\"97\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-17.png 550w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-17-300x111.png 300w\" sizes=\"auto, (max-width: 262px) 100vw, 262px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Case II: Positif Number and Smaller Negatif number<\/h4>\n\n\n\n<p>Contoh: +9 dan -4<\/p>\n\n\n\n<p>Langkah 1 : mencari komplemen 2 dari -4<\/p>\n\n\n\n<p><\/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\/02\/image-18.png\" alt=\"Penjumlahan positif dan negatif\" class=\"wp-image-164\" width=\"103\" height=\"100\"\/><\/figure>\n\n\n\n<p> Langkah 2 : Menjumlahkan +9 dengan C&#8217;2 -4<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"235\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-19-1024x235.png\" alt=\"Penjumlahan dengan Komplemen 2\" class=\"wp-image-165\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-19-1024x235.png 1024w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-19-300x69.png 300w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-19-768x177.png 768w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-19.png 1035w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>Pada kasus ini, sign bit dari addend (penambah) adalah 1. Hasil dari penjumlahan menghasilkan sebuah carry pada bagian akhir, dan carry ini diabaikan. Sehingga hasil akhirnya 0 0101 (+5).<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Case III: Positive Number and Larger Negative Number<\/h4>\n\n\n\n<p>Contoh : -9 dan +4<\/p>\n\n\n\n<p>Langkah 1 : mencari komplemen 2 dari -9<\/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\/02\/image-20.png\" alt=\"Komplemen 2 dari -9\" class=\"wp-image-167\" width=\"109\" height=\"103\"\/><\/figure>\n\n\n\n<p>Langkah 2 : menjumlahkan C&#8217;s 2 dari -9 dan +4<\/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\/02\/image-21.png\" alt=\"\" class=\"wp-image-168\" width=\"255\" height=\"89\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-21.png 531w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-21-300x105.png 300w\" sizes=\"auto, (max-width: 255px) 100vw, 255px\" \/><\/figure>\n\n\n\n<p>Dari hasil diperoleh 1 1011, dimana sign bitnya adalah 1 sehingga bilangannya adalah negatif. Magnitudenya merupakan hasil komplemen 2 yaitu 1011, sehingga bilangan aslinya adalah:<\/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\/02\/image-22.png\" alt=\"Penjumlahan bilangan biner\" class=\"wp-image-169\" width=\"188\" height=\"99\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-22.png 314w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-22-300x159.png 300w\" sizes=\"auto, (max-width: 188px) 100vw, 188px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Case IV: Two Negative Number<\/h4>\n\n\n\n<p>Contoh: -9 dan -4<\/p>\n\n\n\n<p>Langkah 1 : Mencari komplemen 2 dari -9<\/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\/02\/image-23.png\" alt=\"Penjumlahan Bilangan biner\" class=\"wp-image-170\" width=\"106\" height=\"99\"\/><\/figure>\n\n\n\n<p>Langkah 2 : Mencari nilai komplemen 2 dari -4<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"449\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-24-1024x449.png\" alt=\"Penjumlahan Bilangan Biner\" class=\"wp-image-171\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-24-1024x449.png 1024w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-24-300x132.png 300w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-24-768x337.png 768w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-24.png 1078w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>Dari hasil diperoleh 1 1 0011, dimana 1 bit carry diabaikan, sign bitnya adalah 1 sehingga bilangannya adalah negatif. Magnitudenya merupakan hasil komplemen 2 yaitu 0011, sehingga bilangan aslinya adalah :<\/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\/02\/image-25.png\" alt=\"Penjumlahan Bilangan Biner\" class=\"wp-image-172\" width=\"192\" height=\"100\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-25.png 324w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-25-300x156.png 300w\" sizes=\"auto, (max-width: 192px) 100vw, 192px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Case V: Equal and Opposite Numbers<\/h4>\n\n\n\n<p>Contoh: +9 dan -9<\/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\/02\/image-26.png\" alt=\"Penjumlahan bilangan biner\" class=\"wp-image-173\" width=\"287\" height=\"112\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-26.png 545w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-26-300x118.png 300w\" sizes=\"auto, (max-width: 287px) 100vw, 287px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"949\" height=\"240\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-27.png\" alt=\"Penjumlahan bilangan biner\" class=\"wp-image-174\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-27.png 949w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-27-300x76.png 300w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-27-768x194.png 768w\" sizes=\"auto, (max-width: 949px) 100vw, 949px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Operasi Bilangan Biner &#8211;  Perkalian Bilangan Biner<\/h2>\n\n\n\n<p>Perkalaian bilangan biner dilakukan dengan cara yang sama dengan perkalian bilangan disimal. Proses menjadi lebih sederhana karena kita hanya mengalikan digit 1 dengan digit 0, dan tidak melibatkan digit lainnya.<\/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\/02\/image-28.png\" alt=\"Perkalian Bilangan Biner\" class=\"wp-image-177\" width=\"264\" height=\"167\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-28.png 517w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-28-300x191.png 300w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/figure>\n\n\n\n<p>Pada sebagian mesin digital, penjumlahan hanya dapat dilakukan  antara 2 bilangan biner pada satu waktu, sehingga selama perkalian, maka penjumlahan tidak dilakukan  seluruhnya pada satu waktu, tetapi penjumlahan dilakukan untuk 2 partial products per satuan waktunya. Pertama ditambah dengan kedua, hasilnya ditambah dengan ketiga, dan seterusnya seperti ilustrasi di bawah ini.<\/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\/02\/image-29.png\" alt=\"Perkalian Bilangan Binner\" class=\"wp-image-180\" width=\"492\" height=\"238\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-29.png 914w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-29-300x145.png 300w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-29-768x372.png 768w\" sizes=\"auto, (max-width: 492px) 100vw, 492px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Operasi Bilangan Biner &#8211;  Pembagian Bilangan Biner <\/h2>\n\n\n\n<p>Proses pembagian bilangan biner (devidend) dengan bilangan biner lainnya (devisor) sama dengan pembagian pada bilangan desimal. Prosesnya lebih sederhana dalam bilangan biner karena nilai yang dilibatkan hanya 0 dan 1.<\/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\/02\/image-30.png\" alt=\"Pembagian bilangan biner\" class=\"wp-image-181\" width=\"246\" height=\"131\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-30.png 452w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2020\/02\/image-30-300x160.png 300w\" sizes=\"auto, (max-width: 246px) 100vw, 246px\" \/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<p>baca juga artikel Sistem Digital:  <a href=\"https:\/\/ekomartantoh.net\/artikel\/2020\/02\/20\/jenis-jenis-dan-konversi-sistem-bilangan\/\">https:\/\/ekomartantoh.net\/artikel\/2020\/02\/20\/jenis-jenis-dan-konversi-sistem-bilangan\/<\/a> <\/p>\n\n\n\n<p>Visit my other website:  <a href=\"http:\/\/masjidalfajar.com\/\">http:\/\/masjidalfajar.com\/<\/a> <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Operasi bilangan biner akan membahas beberapa point seperti operasi penjumlahan bilangan biner, perkalian bilangan biner dan pembagian bilangan biner. Operasi Bilangan Biner &#8211; Penjumlahan Ada beberapa hal umum yang harus diketahui dalam penjumlahan bilangan biner yaitu sebagai berikut: 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + [&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-155","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>Operasi Bilangan Biner dan Komplemen - eko&#039;s Article<\/title>\n<meta name=\"description\" content=\"Membahas operasi bilangan biner dan komplemen, penjumlahan bilangan biner, komplemen, perkalian bilangan biner, dan pembagian bilangan biner\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/ekomartantoh.net\/artikel\/2020\/02\/23\/operasi-bilangan-biner-dan-koplemen\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Operasi Bilangan Biner dan Komplemen - 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