{"id":743,"date":"2023-09-20T07:58:03","date_gmt":"2023-09-20T07:58:03","guid":{"rendered":"https:\/\/ekomartantoh.net\/artikel\/?p=743"},"modified":"2023-12-23T23:18:08","modified_gmt":"2023-12-23T23:18:08","slug":"sistem-bilangan-operasi-aritmatika","status":"publish","type":"post","link":"https:\/\/ekomartantoh.net\/artikel\/2023\/09\/20\/sistem-bilangan-operasi-aritmatika\/","title":{"rendered":"SISTEM BILANGAN, OPERASI ARITMATIKA"},"content":{"rendered":"\n<p>Sistem bilangan, operasi aritmatika dan pengkodean merupakan materi dasar yang perlu dipahami sebelum kita mempelajari lebih dalam mengenai organsisasi sistem komputer.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">REPRESENTASI DATA pada Sistem Bilangan<\/h2>\n\n\n\n<p>Data : bilangan biner atau informasi berkode biner lain yang dioperasikan untuk mencapai beberapa hasil penghitungan penghitungan aritmatik, pemrosesan data dan operasi logika.<\/p>\n\n\n\n<p>Tipe data :<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Data Numerik : merepresentasikan integer dan pecahan fixed-point, real floating-point dan desimal berkode biner.<\/li>\n\n\n\n<li>Data Logikal : digunakan oleh operasi logika dan untuk menentukan atau memriksa kondisi seperti yang dibutuhkan untuk instruksi bercabang kondisi. <\/li>\n\n\n\n<li>Data bit-tunggal : untuk operasi seperti SHIFT, CLEAR dan TEST.<\/li>\n\n\n\n<li>Data Alfanumerik : data yang tidak hanya dikodekan dengan bilangan tetapi juga dengan huruf dari alpabet dan karakter khusus lainnya.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">SISTEM BILANGAN<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>BINER (radiks \/ basis 2)<br>\u0001 Notasi : (n)2<br>\u0001 Simbol : angka 0 dan 1<\/li>\n\n\n\n<li>OKTAL (radiks \/ basis 8)<br>\u0001 Notasi : (n)8<br>\u0001 Simbol : angka 0, 1, 2, 3, 4, 5, 6, 7<\/li>\n\n\n\n<li>DESIMAL (radiks \/ basis 10)<br>\u0001 Notasi : (n)10<br>\u0001 Simbol : angka 0, 1, 2, 3, 4, 5, 6, 7, 8, 9<\/li>\n\n\n\n<li>HEKSADESIMAL (radiks \/ basis 16)<br>\u0001 Notasi : (n)16<br>\u0001 Simbol : angka 0,1,2,3,4,5,6,7,8,9,A,B, C,D,E,F<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">KONVERSI SISTEM BILANGAN<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Basis X ke DESIMAL<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Bilangan bulat :<\/strong> bilangan tersebut dikalikan dengan<br>X<sup>m<\/sup> (m : sesuai dengan nilai tempat\/bobot).<\/li>\n\n\n\n<li>Contoh : 145<sub>8<\/sub> = \u2026\u2026..<sub>10<\/sub><br>145<sub>8<\/sub> = 1&#215;8<sup>2<\/sup>+4&#215;8<sup>1<\/sup>+5&#215;8<sup>0<\/sup> = 64 + 32 + 5<br>         = 101<sub>10<\/sub><\/li>\n\n\n\n<li><strong>Bilangan pecahan :<\/strong> bilangan tersebut dikalikan<br>dengan X<sup>-m<\/sup> (m: sesuai dengan nilai tempat\/bobot).<\/li>\n\n\n\n<li>Contoh : 0,128 = \u2026\u2026..<sub>10<\/sub><br>0,12 = 1&#215;8<sup>-1<\/sup>+2&#215;8<sup>-2<\/sup><br>= 1\/8+ 2\/64 = 1\/8 + 1\/32 = 5\/32<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><strong>DESIMAL ke Basis X<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Bilangan bulat : <\/strong>bilangan tersebut dibagi berulang dengan basis X<\/li>\n\n\n\n<li><strong>Bilangan pecahan :<\/strong> bilangan tersebut dikalikan dengan basisnya, dan berulang untuk hasil kali<br>pecahannya.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><strong>BASIS X ke BASIS Y<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Bilangan tersebut diubah ke desimal (lihat no. 1) kemudian ubah desimal tersebut ke basis Y (lihat no. 2).<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">REPRESENTASI BILANGAN<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Dinyatakan dengan <strong>sign<\/strong>, bilangan <strong>magnitude<\/strong> dan <strong>posisi titik radiks<\/strong>.<\/li>\n\n\n\n<li>Titik radiks memisahkan bilangan bulat dan pecahan.<\/li>\n\n\n\n<li>Penggunaan titik radiks berkaitan dengan jajaran bilangan yang dapat ditampung oleh komputer.<\/li>\n\n\n\n<li>Representasi <strong>Fixed-point<\/strong> : titik radiks selalu pada posisi tetap.<\/li>\n\n\n\n<li>Representasi Floating-point :<br>           <strong>a = m x r<sup>e<\/sup><\/strong><br>r = radiks, m = mantissa, e = eksponen<br>Untuk menyatakan bilangan yang sangat besar atau sangat kecil, dengan menggeser titik radiks dan mengubah eksponen untuk mempertahankan nilainya.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">ARITMATIKA FIXED POINT<\/h3>\n\n\n\n<p>PENJUMLAHAN dan PENGURANGAN dalam Desimal<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"296\" height=\"85\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-8.png\" alt=\"Penjumlahan dan pengurangan bilangan desimal dalam sistem bilangan\" class=\"wp-image-744\"\/><\/figure>\n\n\n\n<p>PENJUMLAHAN dan PENGURANGAN dalam Basis X<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"418\" height=\"106\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-10.png\" alt=\"PENJUMLAHAN dan PENGURANGAN dalam Basis X pada sistem bilangan\" class=\"wp-image-747\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-10.png 418w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-10-300x76.png 300w\" sizes=\"auto, (max-width: 418px) 100vw, 418px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">ARITMATIKA FLOATING POINT<\/h3>\n\n\n\n<p>Penambahan dan Pengurangan<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"366\" height=\"198\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-11.png\" alt=\"Penambahan dan pengurangan pecahan pada Sistem Bilangan\" class=\"wp-image-749\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-11.png 366w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-11-300x162.png 300w\" sizes=\"auto, (max-width: 366px) 100vw, 366px\" \/><\/figure>\n\n\n\n<p>Perkalian<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"466\" height=\"92\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-12.png\" alt=\"Perkalian pesahan\" class=\"wp-image-750\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-12.png 466w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-12-300x59.png 300w\" sizes=\"auto, (max-width: 466px) 100vw, 466px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Representasi Bilangan Positif dan Negatif pada bilangan BINER<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Label tanda konvensional : + dan \u2013<br>Contoh : +4 dan -4<\/li>\n\n\n\n<li>Menggunakan posisi digit sebelah kiri (MSB) sebagai sign digit (0 untuk positif dan 1 untuk negatif).<br>Contoh : Sign-Magnitude +9 dalam 8 bit = <strong>0<\/strong>0001001<br>               Sign-Magnitude \u20134 dalam 4 bit = <strong>1<\/strong>100<br>Magnitude dari bilangan positif dan negatif sama hanya berbeda pada sign digitnya\/MSB.<\/li>\n\n\n\n<li>Representasi Komplemen-1<br>Angka nol diubah menjadi satu dan satu menjadi nol.<br>Contoh : Dalam 8 bit<br>+12 = 00001100<br>-12 = 11110011<\/li>\n\n\n\n<li>Representasi Komplemen-2<br>Dengan representasi komplemen-1 ditambah 1.<br>Contoh : Dalam 8 bit<br>               <img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"83\" class=\"wp-image-751\" style=\"width: 300px;\" src=\"http:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-13.png\" alt=\"Komplemen-2\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-13.png 320w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-13-300x83.png 300w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">PENJUMLAHAN dan PENGURANGAN dengan Komplemen-2<\/h3>\n\n\n\n<p>Bilangan 6 bit :<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"487\" height=\"357\" src=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-14.png\" alt=\"\" class=\"wp-image-752\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-14.png 487w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-14-300x220.png 300w\" sizes=\"auto, (max-width: 487px) 100vw, 487px\" \/><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\">KODE BINER<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>BCD (Binary Coded Decimal)\n<ul class=\"wp-block-list\">\n<li>Mengkodekan setiap digit desimal dengan 4 bit.<\/li>\n\n\n\n<li>Disebut juga kode 8421 artinya MSB mempunyai bobot 8, sedang LSB mempunyai bobot 1.<\/li>\n\n\n\n<li>Contoh : BCD untuk 4 adalah : 0100<br>                : BCD untuk 18 adalah : 0001 1000<br>                <img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"48\" class=\"wp-image-753\" style=\"width: 300px;\" src=\"http:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-15.png\" alt=\"contoh bcd\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-15.png 354w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-15-300x48.png 300w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>Kode Gray\n<ul class=\"wp-block-list\">\n<li>Kenaikan hitungan (penambahan) dilakukan hanya dengan pengubahan keadaan satu bit saja. <\/li>\n\n\n\n<li>Contoh : Jika 210 dikodekan ke gray adalah \u2026.<br>Caranya : ubah desimal ke biner dahulu (0010)<br>                  <img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"91\" class=\"wp-image-754\" style=\"width: 300px;\" src=\"http:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-16.png\" alt=\"kode gray\" srcset=\"https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-16.png 338w, https:\/\/ekomartantoh.net\/artikel\/wp-content\/uploads\/2023\/09\/image-16-300x91.png 300w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/li>\n\n\n\n<li>Kode Gray sering digunakan dalam situasi dimana kode biner yang lainnya mungkin menghasilkan kesalahan atau kebingungan selama dalam transisi dari satu word kode ke word kode yang lainnya, dimana lebih dari satu bit dari kode diubah.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>KODE ASCII\n<ul class=\"wp-block-list\">\n<li>Kode ASCII termasuk kode Alfanumerik<\/li>\n\n\n\n<li>Contoh : cari kode heksadesimal dan biner untuk huruf b dalam kode ASCII.<br>Cari b dalam tabel Kode ASCII <br>nilai barisnya adalah (6)16 = (0110)2 dan nilai kolomnya adalah (2)16 = (0010)2. Jadi<br>kode ASCII untuk b adalah (62)16 atau (01100010)2.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p><\/p>\n\n\n\n<p>Materi Organisasi Sistem Komputer (OSK):<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><a href=\"http:\/\/ekomartantoh.net\/artikel\/2023\/09\/17\/organisasi-sistem-komputer\/\">Pendahuluan<\/a><\/li>\n\n\n\n<li>Sistem Bilangan<\/li>\n\n\n\n<li><a href=\"https:\/\/ekomartantoh.net\/artikel\/2023\/09\/30\/rangkaian-logika\/\">Rangkaian Logika<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/ekomartantoh.net\/artikel\/2023\/10\/07\/organisasi-komputer-dasar\/\">Organisasi Komputer Dasar<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/ekomartantoh.net\/artikel\/2023\/12\/23\/komputer-pipeline\/\">Komputer Pipeline<\/a><\/li>\n<\/ol>\n\n\n\n<p>My Youtube Channel: <a href=\"https:\/\/www.youtube.com\/@ekomartantoh\">https:\/\/www.youtube.com\/@ekomartantoh<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sistem bilangan, operasi aritmatika dan pengkodean merupakan materi dasar yang perlu dipahami sebelum kita mempelajari lebih dalam mengenai organsisasi sistem komputer. REPRESENTASI DATA pada Sistem Bilangan Data : bilangan biner atau informasi berkode biner lain yang dioperasikan untuk mencapai beberapa hasil penghitungan penghitungan aritmatik, pemrosesan data dan operasi logika. Tipe data : SISTEM BILANGAN KONVERSI [&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":[73],"tags":[76,77,74,78,75,48],"class_list":["post-743","post","type-post","status-publish","format-standard","hentry","category-organisasi-sistem-komputer","tag-bilangan-biner","tag-komplemen","tag-organisasi-sistem-komputer","tag-representasi-bilangan","tag-sistem-bilangan","tag-sistem-operasi"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>SISTEM BILANGAN, OPERASI ARITMATIKA eko&#039;s Article<\/title>\n<meta name=\"description\" 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