{"id":193220,"date":"2025-02-19T07:43:09","date_gmt":"2025-02-19T07:43:09","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=193220"},"modified":"2025-02-19T07:43:12","modified_gmt":"2025-02-19T07:43:12","slug":"convert-decimal-49-and-29-to-binary-using-the-signed-2s-compliment-representation-and-enough-digits-to-accommodate-the-numbers","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/19\/convert-decimal-49-and-29-to-binary-using-the-signed-2s-compliment-representation-and-enough-digits-to-accommodate-the-numbers\/","title":{"rendered":"Convert decimal +49 and +29 to binary, using the signed-2\u2019s-compliment representation and enough digits to accommodate the numbers"},"content":{"rendered":"\n<p>Convert decimal +49 and +29 to binary, using the signed-2\u2019s-compliment representation and enough digits to accommodate the numbers. Then perform the binary equivalent of (+29)+(-49), (-29)+(+49), and (-29)+(-49). Convert the answers back to decimal and verify that they are correct.<\/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>Let&#8217;s break this down into clear steps.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Convert Decimal Numbers to Binary Using 2\u2019s Complement Representation<\/h3>\n\n\n\n<p>We&#8217;ll start by converting both +49 and +29 to binary using 8 bits (since the largest value between +49 and +29 is 49, which can be accommodated within 8 bits).<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Convert +49 to binary:<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Convert the absolute value of 49 to binary:<br>49 in decimal = <strong>110001<\/strong> in binary.<\/li>\n\n\n\n<li>To fit this into 8 bits, we add leading zeros:<br>+49 = <strong>00110001<\/strong> in 8-bit binary.<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Convert +29 to binary:<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Convert the absolute value of 29 to binary:<br>29 in decimal = <strong>11101<\/strong> in binary.<\/li>\n\n\n\n<li>To fit this into 8 bits, we add leading zeros:<br>+29 = <strong>00011101<\/strong> in 8-bit binary.<\/li>\n<\/ol>\n\n\n\n<p>Now, let&#8217;s look at the 2\u2019s complement of the negative numbers.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Convert -49 to binary (using 2&#8217;s complement):<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Start with the binary representation of +49 (<strong>00110001<\/strong>).<\/li>\n\n\n\n<li>Invert the bits (1\u2019s complement): <strong>11001110<\/strong>.<\/li>\n\n\n\n<li>Add 1 to the result (2\u2019s complement): <strong>11001111<\/strong>.<br>So, -49 = <strong>11001111<\/strong> in 8-bit binary.<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Convert -29 to binary (using 2&#8217;s complement):<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Start with the binary representation of +29 (<strong>00011101<\/strong>).<\/li>\n\n\n\n<li>Invert the bits (1\u2019s complement): <strong>11100010<\/strong>.<\/li>\n\n\n\n<li>Add 1 to the result (2\u2019s complement): <strong>11100011<\/strong>.<br>So, -29 = <strong>11100011<\/strong> in 8-bit binary.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Perform the Binary Operations<\/h3>\n\n\n\n<p>Now, we perform the binary additions using 2\u2019s complement for the operations:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>(+29) + (-49):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>+29 = <strong>00011101<\/strong><\/li>\n\n\n\n<li>-49 = <strong>11001111<\/strong><\/li>\n\n\n\n<li>Adding them:<br>&#8220;`<br>00011101<\/li>\n\n\n\n<li>11001111<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<pre class=\"wp-block-code\"><code> 11101100\n ```\n Result = **11101100** (in binary). In decimal, this is -20 (as we convert from 2\u2019s complement).<\/code><\/pre>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li><strong>(-29) + (+49):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>-29 = <strong>11100011<\/strong><\/li>\n\n\n\n<li>+49 = <strong>00110001<\/strong><\/li>\n\n\n\n<li>Adding them:<br>&#8220;`<br>11100011<\/li>\n\n\n\n<li>00110001<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<pre class=\"wp-block-code\"><code> 10010100\n ```\n Result = **10010100** (in binary). In decimal, this is +20 (as we convert from 2\u2019s complement).<\/code><\/pre>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li><strong>(-29) + (-49):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>-29 = <strong>11100011<\/strong><\/li>\n\n\n\n<li>-49 = <strong>11001111<\/strong><\/li>\n\n\n\n<li>Adding them:<br>&#8220;`<br>11100011<\/li>\n\n\n\n<li>11001111<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<pre class=\"wp-block-code\"><code> 10110010\n ```\n Result = **10110010** (in binary). In decimal, this is -78 (as we convert from 2\u2019s complement).<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Convert the Results Back to Decimal<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>11101100<\/strong> (binary) = -20 (decimal)<\/li>\n\n\n\n<li><strong>10010100<\/strong> (binary) = +20 (decimal)<\/li>\n\n\n\n<li><strong>10110010<\/strong> (binary) = -78 (decimal)<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Verify the Results<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>(+29) + (-49) = -20<\/strong>: This is correct.<\/li>\n\n\n\n<li><strong>(-29) + (+49) = +20<\/strong>: This is correct.<\/li>\n\n\n\n<li><strong>(-29) + (-49) = -78<\/strong>: This is correct.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the binary operations and conversions are accurate.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Convert decimal +49 and +29 to binary, using the signed-2\u2019s-compliment representation and enough digits to accommodate the numbers. Then perform the binary equivalent of (+29)+(-49), (-29)+(+49), and (-29)+(-49). Convert the answers back to decimal and verify that they are correct. The Correct Answer and Explanation is : Let&#8217;s break this down into clear steps. Step [&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-193220","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193220","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=193220"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193220\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=193220"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=193220"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=193220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}