{"id":191030,"date":"2025-02-14T05:24:29","date_gmt":"2025-02-14T05:24:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=191030"},"modified":"2025-02-14T05:24:31","modified_gmt":"2025-02-14T05:24:31","slug":"perform-the-following-conversions","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/14\/perform-the-following-conversions\/","title":{"rendered":"Perform the following conversions"},"content":{"rendered":"\n<p>Perform the following conversions:<br>a. 101010 (base 2) to base 10<br>b. CA (base 16) to base 10<br>c. 10101011 (base 2) to base 16<br>Answer<br>Answer<br>d. 50 (base 10) to base 2<br>e. F8 (base 16) to base 2<br>Answer<br>Answer<br>f. Perform the following addition of two binary (base 2) numbers. Your answer should be a number in binary.<br>101110 = ?<\/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<h3 class=\"wp-block-heading\">Binary and Hexadecimal Conversions<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">a. Convert <strong>101010<\/strong> (base 2) to base 10:<\/h4>\n\n\n\n<p>To convert a binary number to decimal, we sum the products of each bit with powers of 2.<\/p>\n\n\n\n<p>[<br>101010_2 = (1 \\times 2^5) + (0 \\times 2^4) + (1 \\times 2^3) + (0 \\times 2^2) + (1 \\times 2^1) + (0 \\times 2^0)<br>]<\/p>\n\n\n\n<p>[<br>= (1 \\times 32) + (0 \\times 16) + (1 \\times 8) + (0 \\times 4) + (1 \\times 2) + (0 \\times 1)<br>]<\/p>\n\n\n\n<p>[<br>= 32 + 0 + 8 + 0 + 2 + 0 = 42<br>]<\/p>\n\n\n\n<p><strong>Answer:<\/strong> ( 42_{10} )<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">b. Convert <strong>CA<\/strong> (base 16) to base 10:<\/h4>\n\n\n\n<p>Each digit in hexadecimal represents a power of 16.<\/p>\n\n\n\n<p>[<br>CA_{16} = (C \\times 16^1) + (A \\times 16^0)<br>]<\/p>\n\n\n\n<p>Since <strong>C = 12<\/strong> and <strong>A = 10<\/strong> in decimal:<\/p>\n\n\n\n<p>[<br>(12 \\times 16) + (10 \\times 1) = 192 + 10 = 202<br>]<\/p>\n\n\n\n<p><strong>Answer:<\/strong> ( 202_{10} )<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">c. Convert <strong>10101011<\/strong> (base 2) to base 16:<\/h4>\n\n\n\n<p>To convert binary to hexadecimal, we group bits in sets of four from right:<\/p>\n\n\n\n<p>[<br>1010\\ 1011<br>]<\/p>\n\n\n\n<p>Each group converts to hex:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>1010<\/strong> (binary) = <strong>A<\/strong> (hex)<\/li>\n\n\n\n<li><strong>1011<\/strong> (binary) = <strong>B<\/strong> (hex)<\/li>\n<\/ul>\n\n\n\n<p><strong>Answer:<\/strong> ( AB_{16} )<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">d. Convert <strong>50<\/strong> (base 10) to base 2:<\/h4>\n\n\n\n<p>Divide 50 by 2 and record the remainders:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Division<\/th><th>Quotient<\/th><th>Remainder<\/th><\/tr><\/thead><tbody><tr><td>50 \u00f7 2<\/td><td>25<\/td><td>0<\/td><\/tr><tr><td>25 \u00f7 2<\/td><td>12<\/td><td>1<\/td><\/tr><tr><td>12 \u00f7 2<\/td><td>6<\/td><td>0<\/td><\/tr><tr><td>6 \u00f7 2<\/td><td>3<\/td><td>0<\/td><\/tr><tr><td>3 \u00f7 2<\/td><td>1<\/td><td>1<\/td><\/tr><tr><td>1 \u00f7 2<\/td><td>0<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Reading from bottom to top: <strong>110010\u2082<\/strong><\/p>\n\n\n\n<p><strong>Answer:<\/strong> ( 110010_2 )<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">e. Convert <strong>F8<\/strong> (base 16) to base 2:<\/h4>\n\n\n\n<p>Each hex digit represents 4 bits:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>F = 1111<\/strong> (binary)<\/li>\n\n\n\n<li><strong>8 = 1000<\/strong> (binary)<\/li>\n<\/ul>\n\n\n\n<p><strong>Answer:<\/strong> ( 11111000_2 )<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">f. Perform binary addition: <strong>101110\u2082 + ?<\/strong><\/h4>\n\n\n\n<p>You didn\u2019t specify the second number, so I assume <strong>101110\u2082 + 1\u2082<\/strong>.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>  101110\n+      1\n---------\n  101111<\/code><\/pre>\n\n\n\n<p><strong>Explanation (300 words):<\/strong><br>Binary addition follows similar rules as decimal addition, but since there are only two digits (0 and 1), the carry system works differently:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>0 + 0 = 0<\/strong><\/li>\n\n\n\n<li><strong>0 + 1 = 1<\/strong><\/li>\n\n\n\n<li><strong>1 + 0 = 1<\/strong><\/li>\n\n\n\n<li><strong>1 + 1 = 10<\/strong> (write 0, carry 1)<\/li>\n\n\n\n<li><strong>1 + 1 + 1 = 11<\/strong> (write 1, carry 1)<\/li>\n<\/ul>\n\n\n\n<p>Let&#8217;s add <strong>101110\u2082 + 1\u2082<\/strong> step by step:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Rightmost bit: <strong>0 + 1 = 1<\/strong> (no carry)<\/li>\n\n\n\n<li>Next bit: <strong>1 + 0 = 1<\/strong><\/li>\n\n\n\n<li>Next bit: <strong>1 + 0 = 1<\/strong><\/li>\n\n\n\n<li>Next bit: <strong>0 + 0 = 0<\/strong><\/li>\n\n\n\n<li>Next bit: <strong>1 + 0 = 1<\/strong><\/li>\n\n\n\n<li>Leftmost bit: <strong>1 + 0 = 1<\/strong><\/li>\n<\/ol>\n\n\n\n<p>So, the sum is <strong>101111\u2082<\/strong>.<\/p>\n\n\n\n<p>This method can be extended to multi-bit binary numbers. If the numbers were larger, we&#8217;d continue carrying over until we processed all bits.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>Let me know if you need more explanation! \ud83d\ude0a<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Perform the following conversions:a. 101010 (base 2) to base 10b. CA (base 16) to base 10c. 10101011 (base 2) to base 16AnswerAnswerd. 50 (base 10) to base 2e. F8 (base 16) to base 2AnswerAnswerf. Perform the following addition of two binary (base 2) numbers. Your answer should be a number in binary.101110 = ? 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-191030","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191030","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=191030"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/191030\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=191030"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=191030"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=191030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}