{"id":199951,"date":"2025-03-13T05:24:22","date_gmt":"2025-03-13T05:24:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=199951"},"modified":"2025-03-13T05:24:24","modified_gmt":"2025-03-13T05:24:24","slug":"what-range-of-signed-decimal-values-can-be-represented-in-12-bits-including-the-sign-bit","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/13\/what-range-of-signed-decimal-values-can-be-represented-in-12-bits-including-the-sign-bit\/","title":{"rendered":"What range of signed decimal values can be represented in 12 bits (including the sign bit)"},"content":{"rendered":"\n<p>What range of signed decimal values can be represented in 12 bits (including the sign bit)?<\/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>In a 12-bit signed binary system, one bit is reserved for the sign (positive or negative), and the remaining 11 bits are used to represent the magnitude of the number. This system typically uses a two&#8217;s complement representation, which is a method for encoding signed integers in binary form. The two&#8217;s complement system is efficient because it allows for easy arithmetic operations and simplifies the representation of negative numbers.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Range of Signed Decimal Values:<\/h3>\n\n\n\n<p>In a 12-bit system, the first bit (leftmost) is the sign bit. A <code>0<\/code> in the sign bit represents a positive number, and a <code>1<\/code> represents a negative number. The remaining 11 bits are used to represent the magnitude of the number.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Positive Range<\/strong>: The largest positive value occurs when the sign bit is <code>0<\/code> and all other bits are set to <code>1<\/code>. In binary, this is <code>011111111111<\/code>, which equals to: [<br>2^{11} &#8211; 1 = 2047<br>]<\/li>\n\n\n\n<li><strong>Negative Range<\/strong>: The smallest negative value occurs when the sign bit is <code>1<\/code> and all other bits are set to <code>0<\/code> (in two&#8217;s complement, the number with a leading <code>1<\/code> represents a negative number). This value is: [<br>-2^{11} = -2048<br>]<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the <strong>range<\/strong> of signed decimal values that can be represented in a 12-bit signed binary system is from <strong>-2048<\/strong> to <strong>2047<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Two&#8217;s Complement Representation:<\/h3>\n\n\n\n<p>In two&#8217;s complement, to represent a negative number, you subtract the magnitude from the maximum possible value (which is ( 2^{n-1} ), where ( n ) is the total number of bits). For example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To represent <code>-1<\/code> in 12-bit, the binary value is <code>111111111111<\/code> (all bits are set to <code>1<\/code>).<\/li>\n\n\n\n<li>To represent <code>-2048<\/code> in 12-bit, the binary value is <code>100000000000<\/code>.<\/li>\n<\/ul>\n\n\n\n<p>The two&#8217;s complement method provides an elegant solution for representing both positive and negative numbers in a fixed bit width, as it eliminates the need for separate representations for positive and negative numbers, streamlining arithmetic operations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What range of signed decimal values can be represented in 12 bits (including the sign bit)? The correct answer and explanation is : In a 12-bit signed binary system, one bit is reserved for the sign (positive or negative), and the remaining 11 bits are used to represent the magnitude of the number. This system [&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-199951","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199951","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=199951"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199951\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199951"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199951"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199951"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}