{"id":167791,"date":"2024-11-16T07:33:21","date_gmt":"2024-11-16T07:33:21","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=167791"},"modified":"2024-11-16T07:33:25","modified_gmt":"2024-11-16T07:33:25","slug":"convert-the-decimal-number-32-into-an-8-bit-signed-binary-number","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/16\/convert-the-decimal-number-32-into-an-8-bit-signed-binary-number\/","title":{"rendered":"Convert the decimal number 32 into an 8-bit signed binary number."},"content":{"rendered":"\n<p>Convert the decimal number 32 into an 8-bit signed binary number.<br>a) 10000000<br>b) 00100000<br>c) 11100000<br>d) 11000000<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct answer is:<\/p>\n\n\n\n<p><strong>b) 00100000<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To convert a decimal number into an 8-bit signed binary number, we need to understand how signed numbers are represented in binary. In an 8-bit system, the most significant bit (MSB) is used to represent the sign of the number. If the MSB is 0, the number is positive; if it&#8217;s 1, the number is negative. The remaining 7 bits are used to represent the magnitude of the number.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Step 1: Convert the decimal number to binary.<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>We are given the decimal number <strong>32<\/strong>. To convert it into binary, we repeatedly divide the number by 2 and record the remainders.<\/li>\n\n\n\n<li>32 \u00f7 2 = 16, remainder 0<\/li>\n\n\n\n<li>16 \u00f7 2 = 8, remainder 0<\/li>\n\n\n\n<li>8 \u00f7 2 = 4, remainder 0<\/li>\n\n\n\n<li>4 \u00f7 2 = 2, remainder 0<\/li>\n\n\n\n<li>2 \u00f7 2 = 1, remainder 0<\/li>\n\n\n\n<li>1 \u00f7 2 = 0, remainder 1 Reading the remainders from bottom to top, we get the binary representation of 32 as <strong>100000<\/strong>.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Step 2: Determine the signed binary representation.<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Since <strong>32<\/strong> is positive, the MSB (most significant bit) will be 0.<\/li>\n\n\n\n<li>To fit this into 8 bits, we simply add leading zeros to the binary representation. So, we add two zeros at the beginning of <strong>100000<\/strong> to make it an 8-bit number: <strong>00100000<\/strong>.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Step 3: Verify the options.<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The binary number <strong>00100000<\/strong> corresponds to the decimal number 32 in an 8-bit signed binary system.<\/li>\n\n\n\n<li>Option <strong>b) 00100000<\/strong> is the correct answer.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Why the other options are incorrect:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>a) 10000000<\/strong>: This represents -128 in an 8-bit signed binary system (due to the MSB being 1).<\/li>\n\n\n\n<li><strong>c) 11100000<\/strong>: This represents a negative number, not 32.<\/li>\n\n\n\n<li><strong>d) 11000000<\/strong>: This also represents a negative number and is incorrect for the positive decimal 32.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the correct 8-bit signed binary representation of 32 is <strong>00100000<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Convert the decimal number 32 into an 8-bit signed binary number.a) 10000000b) 00100000c) 11100000d) 11000000 The Correct Answer and Explanation is: The correct answer is: b) 00100000 Explanation: To convert a decimal number into an 8-bit signed binary number, we need to understand how signed numbers are represented in binary. In an 8-bit system, the [&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-167791","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167791","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=167791"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167791\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167791"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167791"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167791"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}