{"id":199953,"date":"2025-03-13T05:25:46","date_gmt":"2025-03-13T05:25:46","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=199953"},"modified":"2025-03-13T05:25:48","modified_gmt":"2025-03-13T05:25:48","slug":"how-many-bits-are-required-to-represent-decimal-values-ranging-from-50-to-50","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/13\/how-many-bits-are-required-to-represent-decimal-values-ranging-from-50-to-50\/","title":{"rendered":"How many bits are required to represent decimal values ranging from-50 to +50"},"content":{"rendered":"\n<p>How many bits are required to represent decimal values ranging from-50 to +50?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To determine how many bits are required to represent decimal values ranging from -50 to +50, we must first understand how binary numbers work and the concept of signed numbers.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Representing Positive Numbers<\/h3>\n\n\n\n<p>To represent the positive values, we begin by calculating how many bits are required to represent the number 50. The highest value in our range is +50, and we need to find the binary representation of 50.<\/p>\n\n\n\n<p>First, convert 50 into binary:<br>50 in decimal is 110010 in binary.<\/p>\n\n\n\n<p>Since 50 is a 6-bit number, we need at least 6 bits to represent numbers from 0 to 50.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Adding Signed Representation (Negative Numbers)<\/h3>\n\n\n\n<p>For signed numbers (which include both positive and negative numbers), we can use a method called &#8220;two&#8217;s complement&#8221; to represent negative values. In two&#8217;s complement, one bit is reserved for the sign of the number. A <code>0<\/code> in the most significant bit (MSB) represents positive numbers, while a <code>1<\/code> in the MSB represents negative numbers.<\/p>\n\n\n\n<p>In this case, the range of values is from -50 to +50. Since the largest magnitude in the range is 50, we need enough bits to represent the number 50 and also represent -50.<\/p>\n\n\n\n<p>For numbers from -50 to +50, the magnitude of the values reaches 50, so we need to represent values from -50 to +50 inclusively. The binary representation of -50 in two&#8217;s complement is 11001110 for 8 bits.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Number of Bits Required<\/h3>\n\n\n\n<p>Therefore, 8 bits are needed to represent numbers from -50 to +50 because:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>6 bits are required to represent the positive number 50.<\/li>\n\n\n\n<li>An additional 1 bit is needed for the sign.<\/li>\n\n\n\n<li>We need 8 bits total for a signed number (including two&#8217;s complement representation).<\/li>\n<\/ol>\n\n\n\n<p>Thus, <strong>8 bits<\/strong> are required to represent decimal values ranging from -50 to +50.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How many bits are required to represent decimal values ranging from-50 to +50? The correct answer and explanation is : To determine how many bits are required to represent decimal values ranging from -50 to +50, we must first understand how binary numbers work and the concept of signed numbers. Step 1: Representing Positive Numbers [&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-199953","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199953","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=199953"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199953\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199953"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199953"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199953"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}