{"id":217318,"date":"2025-05-21T17:31:15","date_gmt":"2025-05-21T17:31:15","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=217318"},"modified":"2025-05-21T17:33:25","modified_gmt":"2025-05-21T17:33:25","slug":"digital-computer-has-a-common-bus-system-for-16-registers-of-32-bits-each","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/21\/digital-computer-has-a-common-bus-system-for-16-registers-of-32-bits-each\/","title":{"rendered":"Digital computer has a common bus system for 16 registers of 32 bits each."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Digital computer has a common bus system for 16 registers of 32 bits each. The bus is constructed with three-state buffer.How many decoders are required for each bit?What will be the size of each decoder?In total, how many three-state buffers are used?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To determine the number of <strong>decoders<\/strong> and <strong>three-state buffers<\/strong> required in a <strong>common bus system<\/strong> for <strong>16 registers of 32 bits each<\/strong>, we need to understand how such a system typically operates.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>1. How Many Decoders Are Required?<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">In a <strong>common bus system<\/strong> using <strong>three-state buffers<\/strong>, two decoders are typically used:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>One decoder for selecting the source register<\/strong> (for reading onto the bus).<\/li>\n\n\n\n<li><strong>One decoder for selecting the destination register<\/strong> (for loading data from the bus).<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Each decoder selects <strong>one of 16 registers<\/strong>, so we need:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>4-to-16 line decoder<\/strong> for <strong>source selection<\/strong><\/li>\n\n\n\n<li>A <strong>4-to-16 line decoder<\/strong> for <strong>destination selection<\/strong><\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u2705 <strong>Number of decoders per bit = 2<\/strong> (shared across all bits, not per bit)<br>\u2705 <strong>Size of each decoder = 4-to-16 line decoder<\/strong><\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>2. How Many Three-State Buffers Are Required in Total?<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Each <strong>bit<\/strong> in every <strong>register<\/strong> must connect to the bus via a <strong>three-state buffer<\/strong>, but <strong>only one register<\/strong> can place its value on the bus at a time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Each register has 32 bits. To output its data to the bus, each bit needs a three-state buffer.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Each of the <strong>16 registers<\/strong> contributes <strong>32 bits<\/strong>.<\/li>\n\n\n\n<li>So:<br>Total&nbsp;three-state&nbsp;buffers=16\u00d732=512\\text{Total three-state buffers} = 16 \\times 32 = 512<\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u2705 <strong>Total three-state buffers = 512<\/strong><\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300 words)<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">In a digital system with a <strong>common bus architecture<\/strong>, multiple registers share a single set of bus lines to transmit and receive data. The <strong>three-state buffer<\/strong> is critical here because it allows multiple registers to be connected to the bus without interference \u2014 only one register drives the bus at any time while others are in a high-impedance (inactive) state.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Each of the 16 registers is 32 bits wide. When a register needs to output data onto the bus, each of its 32 bits must be connected through a three-state buffer. This means each register needs 32 such buffers. Since there are 16 registers, the total number of three-state buffers required is: 16&nbsp;registers\u00d732&nbsp;bits\/register=512&nbsp;three-state&nbsp;buffers16 \\text{ registers} \\times 32 \\text{ bits\/register} = 512 \\text{ three-state buffers}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">These buffers are enabled based on which register is selected to place data on the bus, which is controlled by a decoder. To select one of the 16 registers, a <strong>4-bit binary input<\/strong> is sufficient (since 24=162^4 = 16), so a <strong>4-to-16 line decoder<\/strong> is used. One decoder enables output (source register) while another decoder enables input (destination register).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Each decoder works on a control line, not per bit, and is shared among all 32 bits. Thus, <strong>two 4-to-16 decoders<\/strong> are used, not 32 per bit.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This arrangement minimizes complexity and allows efficient communication between multiple registers using a single bus line structure.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Digital computer has a common bus system for 16 registers of 32 bits each. The bus is constructed with three-state buffer.How many decoders are required for each bit?What will be the size of each decoder?In total, how many three-state buffers are used? The Correct Answer and Explanation is: To determine the number of decoders and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-217318","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217318","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=217318"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217318\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=217318"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=217318"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=217318"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}