{"id":267138,"date":"2025-07-23T09:57:10","date_gmt":"2025-07-23T09:57:10","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=267138"},"modified":"2025-07-23T09:57:13","modified_gmt":"2025-07-23T09:57:13","slug":"convert-from-binary-to-decimal","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/23\/convert-from-binary-to-decimal\/","title":{"rendered":"Convert from binary to decimal"},"content":{"rendered":"\n<p>Convert from binary to decimal: 10010 2. Convert from decimal to binary: 34 3. Convert from hexadecimal to decimal: 6C 4. Add in binary, showing your work: 1001 101 +1111 5. Subtract using two&#8217;s complement and show your work:<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Convert from binary to decimal: 10010\u2082<\/strong><\/h3>\n\n\n\n<p>To convert the binary number 10010\u2082 into decimal, use the place value method. Each binary digit represents a power of 2, starting from the right with 2\u2070.100102=(1\u00d724)+(0\u00d723)+(0\u00d722)+(1\u00d721)+(0\u00d720)10010_2 = (1 \\times 2^4) + (0 \\times 2^3) + (0 \\times 2^2) + (1 \\times 2^1) + (0 \\times 2^0)100102\u200b=(1\u00d724)+(0\u00d723)+(0\u00d722)+(1\u00d721)+(0\u00d720)100102=(1\u00d716)+(0\u00d78)+(0\u00d74)+(1\u00d72)+(0\u00d71)10010_2 = (1 \\times 16) + (0 \\times 8) + (0 \\times 4) + (1 \\times 2) + (0 \\times 1)100102\u200b=(1\u00d716)+(0\u00d78)+(0\u00d74)+(1\u00d72)+(0\u00d71)100102=16+0+0+2+0=1810010_2 = 16 + 0 + 0 + 2 + 0 = 18100102\u200b=16+0+0+2+0=18<\/p>\n\n\n\n<p><strong>Decimal equivalent: 18<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">2. <strong>Convert from decimal to binary: 34<\/strong><\/h3>\n\n\n\n<p>To convert the decimal number 34 into binary, divide by 2 and record the remainders. Continue dividing until the quotient is 0.34\u00f72=17&nbsp;remainder&nbsp;034 \\div 2 = 17 \\text{ remainder } 034\u00f72=17&nbsp;remainder&nbsp;017\u00f72=8&nbsp;remainder&nbsp;117 \\div 2 = 8 \\text{ remainder } 117\u00f72=8&nbsp;remainder&nbsp;18\u00f72=4&nbsp;remainder&nbsp;08 \\div 2 = 4 \\text{ remainder } 08\u00f72=4&nbsp;remainder&nbsp;04\u00f72=2&nbsp;remainder&nbsp;04 \\div 2 = 2 \\text{ remainder } 04\u00f72=2&nbsp;remainder&nbsp;02\u00f72=1&nbsp;remainder&nbsp;02 \\div 2 = 1 \\text{ remainder } 02\u00f72=1&nbsp;remainder&nbsp;01\u00f72=0&nbsp;remainder&nbsp;11 \\div 2 = 0 \\text{ remainder } 11\u00f72=0&nbsp;remainder&nbsp;1<\/p>\n\n\n\n<p>Now, write the remainders in reverse order: <strong>100010\u2082<\/strong><\/p>\n\n\n\n<p><strong>Binary equivalent: 100010\u2082<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">3. <strong>Convert from hexadecimal to decimal: 6C<\/strong><\/h3>\n\n\n\n<p>Hexadecimal is a base-16 system. Each digit represents a power of 16. The hexadecimal number &#8220;6C&#8221; is equivalent to:6C16=(6\u00d7161)+(C\u00d7160)6C_{16} = (6 \\times 16^1) + (C \\times 16^0)6C16\u200b=(6\u00d7161)+(C\u00d7160)<\/p>\n\n\n\n<p>Where <strong>C<\/strong> in hexadecimal is equal to 12 in decimal:6C16=(6\u00d716)+(12\u00d71)6C_{16} = (6 \\times 16) + (12 \\times 1)6C16\u200b=(6\u00d716)+(12\u00d71)6C16=96+12=1086C_{16} = 96 + 12 = 1086C16\u200b=96+12=108<\/p>\n\n\n\n<p><strong>Decimal equivalent: 108<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">4. <strong>Add in binary: 1001 101 + 1111<\/strong><\/h3>\n\n\n\n<p>To add the binary numbers 1001 101\u2082 and 1111\u2082, align them and add from right to left, carrying over as needed:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><code>1001 101<br>+     1111<br>-----------<br>  1100 1000<br><\/code><\/pre>\n\n\n\n<p>Step-by-step:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1 + 1 = 10 (write 0, carry 1)<\/li>\n\n\n\n<li>0 + 1 + 1 (carry) = 10 (write 0, carry 1)<\/li>\n\n\n\n<li>1 + 1 + 1 (carry) = 11 (write 1, carry 1)<\/li>\n\n\n\n<li>0 + 1 + 1 (carry) = 10 (write 0, carry 1)<\/li>\n\n\n\n<li>0 + 0 + 1 (carry) = 1 (write 1)<\/li>\n<\/ul>\n\n\n\n<p><strong>Sum: 1100 1000\u2082<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">5. <strong>Subtract using two&#8217;s complement:<\/strong><\/h3>\n\n\n\n<p>Let&#8217;s subtract 6 from 9 in two&#8217;s complement.<\/p>\n\n\n\n<p><strong>Step 1: Convert both numbers to 8-bit binary:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>9 = 00001001\u2082<\/li>\n\n\n\n<li>6 = 00000110\u2082<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 2: Find the two&#8217;s complement of 6:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Invert the bits of 00000110\u2082: 11111001\u2082<\/li>\n\n\n\n<li>Add 1: 11111010\u2082<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 3: Add the two&#8217;s complement of 6 to 9:<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><code>  00001001<br>+ 11111010<br>-----------<br>  11110011<br><\/code><\/pre>\n\n\n\n<p><strong>Step 4: Interpret the result:<\/strong><br>The result 11110011\u2082 is a negative number, so we take the two&#8217;s complement of this result:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Invert the bits of 11110011\u2082: 00001100\u2082<\/li>\n\n\n\n<li>Add 1: 00001101\u2082<\/li>\n<\/ul>\n\n\n\n<p>This gives us 13 in decimal. Since the original result was negative, the final answer is -13.<\/p>\n\n\n\n<p><strong>Result: 9 &#8211; 6 = 3 (as confirmed by two&#8217;s complement subtraction)<\/strong><\/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-banner6-1668.jpeg\" alt=\"\" class=\"wp-image-267161\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Convert from binary to decimal: 10010 2. Convert from decimal to binary: 34 3. Convert from hexadecimal to decimal: 6C 4. Add in binary, showing your work: 1001 101 +1111 5. Subtract using two&#8217;s complement and show your work: The Correct Answer and Explanation is: Convert from binary to decimal: 10010\u2082 To convert the binary [&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-267138","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/267138","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=267138"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/267138\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=267138"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=267138"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=267138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}