{"id":267164,"date":"2025-07-23T10:00:08","date_gmt":"2025-07-23T10:00:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=267164"},"modified":"2025-07-23T10:00:11","modified_gmt":"2025-07-23T10:00:11","slug":"converting-from-binary-to-decimal","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/23\/converting-from-binary-to-decimal\/","title":{"rendered":"Converting from binary to decimal"},"content":{"rendered":"\n<p>9 points) Converting from binary to decimal: a. (2 points) Convert 10010<br>to decimal. b. (3 points) Convert 110101<br>to decimal. c. (4 points) Convert 11001110<br>to decimal. 7) (9 points) Converting from decimal to binary: a. (2 points) Convert 11<br>to binary. b. (3 points) Convert 43<br>to binary. c. (4 points) Convert 298<br>to binary.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Binary to Decimal Conversions:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">a. Convert 10010210010_2100102\u200b to Decimal:<\/h4>\n\n\n\n<p>To convert binary to decimal, we sum the values of the positions where there is a &#8220;1&#8221;, starting from the rightmost digit. The binary number 10010210010_2100102\u200b can be expanded as: 1\u00d724+0\u00d723+0\u00d722+1\u00d721+0\u00d7201 \\times 2^4 + 0 \\times 2^3 + 0 \\times 2^2 + 1 \\times 2^1 + 0 \\times 2^01\u00d724+0\u00d723+0\u00d722+1\u00d721+0\u00d720 =16+0+0+2+0=18= 16 + 0 + 0 + 2 + 0 = 18=16+0+0+2+0=18<\/p>\n\n\n\n<p>So, 100102=181010010_2 = 18_{10}100102\u200b=1810\u200b.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">b. Convert 1101012110101_21101012\u200b to Decimal:<\/h4>\n\n\n\n<p>For 1101012110101_21101012\u200b, we expand similarly: 1\u00d725+1\u00d724+0\u00d723+1\u00d722+0\u00d721+1\u00d7201 \\times 2^5 + 1 \\times 2^4 + 0 \\times 2^3 + 1 \\times 2^2 + 0 \\times 2^1 + 1 \\times 2^01\u00d725+1\u00d724+0\u00d723+1\u00d722+0\u00d721+1\u00d720 =32+16+0+4+0+1=53= 32 + 16 + 0 + 4 + 0 + 1 = 53=32+16+0+4+0+1=53<\/p>\n\n\n\n<p>So, 1101012=5310110101_2 = 53_{10}1101012\u200b=5310\u200b.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">c. Convert 11001110211001110_2110011102\u200b to Decimal:<\/h4>\n\n\n\n<p>For 11001110211001110_2110011102\u200b, the expansion is: 1\u00d727+1\u00d726+0\u00d725+0\u00d724+1\u00d723+1\u00d722+1\u00d721+0\u00d7201 \\times 2^7 + 1 \\times 2^6 + 0 \\times 2^5 + 0 \\times 2^4 + 1 \\times 2^3 + 1 \\times 2^2 + 1 \\times 2^1 + 0 \\times 2^01\u00d727+1\u00d726+0\u00d725+0\u00d724+1\u00d723+1\u00d722+1\u00d721+0\u00d720 =128+64+0+0+8+4+2+0=206= 128 + 64 + 0 + 0 + 8 + 4 + 2 + 0 = 206=128+64+0+0+8+4+2+0=206<\/p>\n\n\n\n<p>So, 110011102=2061011001110_2 = 206_{10}110011102\u200b=20610\u200b.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Decimal to Binary Conversions:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">a. Convert 111011_{10}1110\u200b to Binary:<\/h4>\n\n\n\n<p>To convert decimal to binary, we repeatedly divide the number by 2, recording the remainders.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>11\u00f72=511 \\div 2 = 511\u00f72=5 remainder 1<\/li>\n\n\n\n<li>5\u00f72=25 \\div 2 = 25\u00f72=2 remainder 1<\/li>\n\n\n\n<li>2\u00f72=12 \\div 2 = 12\u00f72=1 remainder 0<\/li>\n\n\n\n<li>1\u00f72=01 \\div 2 = 01\u00f72=0 remainder 1<\/li>\n<\/ol>\n\n\n\n<p>Now, write the remainders from bottom to top: 1110=1011211_{10} = 1011_21110\u200b=10112\u200b.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">b. Convert 431043_{10}4310\u200b to Binary:<\/h4>\n\n\n\n<p>Following the same method for 431043_{10}4310\u200b:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>43\u00f72=2143 \\div 2 = 2143\u00f72=21 remainder 1<\/li>\n\n\n\n<li>21\u00f72=1021 \\div 2 = 1021\u00f72=10 remainder 1<\/li>\n\n\n\n<li>10\u00f72=510 \\div 2 = 510\u00f72=5 remainder 0<\/li>\n\n\n\n<li>5\u00f72=25 \\div 2 = 25\u00f72=2 remainder 1<\/li>\n\n\n\n<li>2\u00f72=12 \\div 2 = 12\u00f72=1 remainder 0<\/li>\n\n\n\n<li>1\u00f72=01 \\div 2 = 01\u00f72=0 remainder 1<\/li>\n<\/ol>\n\n\n\n<p>Reading the remainders: 4310=101011243_{10} = 101011_24310\u200b=1010112\u200b.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">c. Convert 29810298_{10}29810\u200b to Binary:<\/h4>\n\n\n\n<p>For 29810298_{10}29810\u200b:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>298\u00f72=149298 \\div 2 = 149298\u00f72=149 remainder 0<\/li>\n\n\n\n<li>149\u00f72=74149 \\div 2 = 74149\u00f72=74 remainder 1<\/li>\n\n\n\n<li>74\u00f72=3774 \\div 2 = 3774\u00f72=37 remainder 0<\/li>\n\n\n\n<li>37\u00f72=1837 \\div 2 = 1837\u00f72=18 remainder 1<\/li>\n\n\n\n<li>18\u00f72=918 \\div 2 = 918\u00f72=9 remainder 0<\/li>\n\n\n\n<li>9\u00f72=49 \\div 2 = 49\u00f72=4 remainder 1<\/li>\n\n\n\n<li>4\u00f72=24 \\div 2 = 24\u00f72=2 remainder 0<\/li>\n\n\n\n<li>2\u00f72=12 \\div 2 = 12\u00f72=1 remainder 0<\/li>\n\n\n\n<li>1\u00f72=01 \\div 2 = 01\u00f72=0 remainder 1<\/li>\n<\/ol>\n\n\n\n<p>Reading the remainders from bottom to top: 29810=1001011102298_{10} = 100101110_229810\u200b=1001011102\u200b.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>Binary to decimal involves multiplying each binary digit by 2 raised to the power of its position (starting from 0 for the rightmost bit) and summing the results. Decimal to binary is done by dividing the number by 2, keeping track of the remainders at each step, and reading them from bottom to top to form the binary number. These conversions are fundamental for understanding how data is represented in computers.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1669.jpeg\" alt=\"\" class=\"wp-image-267165\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>9 points) Converting from binary to decimal: a. (2 points) Convert 10010to decimal. b. (3 points) Convert 110101to decimal. c. (4 points) Convert 11001110to decimal. 7) (9 points) Converting from decimal to binary: a. (2 points) Convert 11to binary. b. (3 points) Convert 43to binary. c. (4 points) Convert 298to binary. The Correct Answer and [&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-267164","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/267164","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=267164"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/267164\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=267164"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=267164"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=267164"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}