{"id":179804,"date":"2025-01-02T09:23:06","date_gmt":"2025-01-02T09:23:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=179804"},"modified":"2025-01-02T09:23:08","modified_gmt":"2025-01-02T09:23:08","slug":"convert-the-decimal-number-170-to-binary","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/02\/convert-the-decimal-number-170-to-binary\/","title":{"rendered":"Convert the decimal number 170 to binary"},"content":{"rendered":"\n<p>Convert the decimal number 170 to binary: (Enter all bits next to each other and NO leading zeros!) D Question 2 Convert the hexadecimal number ABC to binary. (Enter all bits next to each other with leading zeros!) Question 3 What is the result of adding these two binary numbers: 10100 + 11 = Notes: . This is not conversion, answer binary number \u2022 Enter all bits next to each other and NO leading zeros!<\/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 address each of your questions step by step:<\/p>\n\n\n\n<p><strong>Question 1: Convert the decimal number 170 to binary.<\/strong><\/p>\n\n\n\n<p>To convert the decimal number 170 to binary, we repeatedly divide the number by 2, recording the remainders:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>170 \u00f7 2 = 85, remainder 0<\/li>\n\n\n\n<li>85 \u00f7 2 = 42, remainder 1<\/li>\n\n\n\n<li>42 \u00f7 2 = 21, remainder 0<\/li>\n\n\n\n<li>21 \u00f7 2 = 10, remainder 1<\/li>\n\n\n\n<li>10 \u00f7 2 = 5, remainder 0<\/li>\n\n\n\n<li>5 \u00f7 2 = 2, remainder 1<\/li>\n\n\n\n<li>2 \u00f7 2 = 1, remainder 0<\/li>\n\n\n\n<li>1 \u00f7 2 = 0, remainder 1<\/li>\n<\/ul>\n\n\n\n<p>Reading the remainders from bottom to top, we get: <strong>10101010<\/strong>.<\/p>\n\n\n\n<p><strong>Question 2: Convert the hexadecimal number ABC to binary.<\/strong><\/p>\n\n\n\n<p>Each hexadecimal digit corresponds to a 4-bit binary number:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A (hex) = 1010 (binary)<\/li>\n\n\n\n<li>B (hex) = 1011 (binary)<\/li>\n\n\n\n<li>C (hex) = 1100 (binary)<\/li>\n<\/ul>\n\n\n\n<p>Therefore, <strong>ABC (hex) = 101010111100 (binary)<\/strong>.<\/p>\n\n\n\n<p><strong>Question 3: What is the result of adding these two binary numbers: 10100 + 11?<\/strong><\/p>\n\n\n\n<p>First, align the binary numbers:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>  10100\n+    11<\/code><\/pre>\n\n\n\n<p>Add them from right to left:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>0 + 1 = 1<\/li>\n\n\n\n<li>0 + 1 = 1<\/li>\n\n\n\n<li>1 + 0 = 1<\/li>\n\n\n\n<li>0 + 0 = 0<\/li>\n\n\n\n<li>1 + 0 = 1<\/li>\n<\/ul>\n\n\n\n<p>The sum is <strong>10111<\/strong>.<\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Decimal to Binary Conversion:<\/strong> The process involves dividing the decimal number by 2 and recording the remainders. This method is based on the fact that each division by 2 shifts the binary representation to the right, effectively determining each bit from least significant to most significant.<\/li>\n\n\n\n<li><strong>Hexadecimal to Binary Conversion:<\/strong> Hexadecimal is a base-16 system, and each digit represents four binary digits (bits). By converting each hexadecimal digit to its 4-bit binary equivalent, we can easily obtain the binary representation of the entire number.<\/li>\n\n\n\n<li><strong>Binary Addition:<\/strong> Binary addition follows the same principles as decimal addition but operates in base-2. The key rules are:<\/li>\n\n\n\n<li>0 + 0 = 0<\/li>\n\n\n\n<li>0 + 1 = 1<\/li>\n\n\n\n<li>1 + 0 = 1<\/li>\n\n\n\n<li>1 + 1 = 10 (which is 0 with a carry of 1)<\/li>\n<\/ul>\n\n\n\n<p>Understanding these fundamental operations is crucial in computer science and digital electronics, as binary and hexadecimal systems are foundational to data representation and processing.<\/p>\n\n\n\n<p>For a visual explanation of converting hexadecimal to binary, you might find the following video helpful:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Convert the decimal number 170 to binary: (Enter all bits next to each other and NO leading zeros!) D Question 2 Convert the hexadecimal number ABC to binary. (Enter all bits next to each other with leading zeros!) Question 3 What is the result of adding these two binary numbers: 10100 + 11 = Notes: [&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-179804","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179804","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=179804"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179804\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=179804"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=179804"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=179804"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}