Convert 1101.01102 to decimal.<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n The given binary number is 1101.01102<\/strong>. Let’s convert it to decimal step by step.<\/p>\n\n\n\n Each digit in a binary number represents a power of 2, starting from the right (2\u2070) and increasing to the left.<\/p>\n\n\n\n [ [ [ The digits after the binary point represent negative powers of 2: [ [ [ [ Thus, 1101.0110\u2082 = 13.375\u2081\u2080<\/strong>.<\/p>\n\n\n\n Binary numbers use base 2, meaning each digit represents powers of 2. To convert a binary number to decimal, we break it into two parts: the integer part (left of the binary point) and the fractional part (right of the binary point).<\/p>\n\n\n\n For the integer part, we multiply each digit by increasing powers of 2, from right to left. The leftmost digit (most significant bit) has the highest power. In 1101\u2082<\/strong>, we multiply each digit by 2\u00b3, 2\u00b2, 2\u00b9,<\/strong> and 2\u2070<\/strong>. This results in 13\u2081\u2080<\/strong>.<\/p>\n\n\n\n For the fractional part, each digit is multiplied by decreasing negative powers of 2. The first digit after the binary point is multiplied by 2\u207b\u00b9 (0.5)<\/strong>, the second by 2\u207b\u00b2 (0.25)<\/strong>, and so on. The sum of these values gives 0.375\u2081\u2080<\/strong>.<\/p>\n\n\n\n Finally, adding both parts results in 13.375\u2081\u2080<\/strong>.<\/p>\n\n\n\n This method works universally for any binary number, ensuring accurate conversion.<\/p>\n","protected":false},"excerpt":{"rendered":" Convert 1101.01102 to decimal. The correct answer and explanation is : The given binary number is 1101.01102. Let’s convert it to decimal step by step. Step 1: Convert the integer part (1101) to decimal Each digit in a binary number represents a power of 2, starting from the right (2\u2070) and increasing to the left. […]<\/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-204754","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/204754","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=204754"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/204754\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=204754"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=204754"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=204754"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Convert the integer part (1101) to decimal<\/strong><\/h3>\n\n\n\n
1101_2 = (1 \u00d7 2^3) + (1 \u00d7 2^2) + (0 \u00d7 2^1) + (1 \u00d7 2^0)
]<\/p>\n\n\n\n
= (1 \u00d7 8) + (1 \u00d7 4) + (0 \u00d7 2) + (1 \u00d7 1)
]<\/p>\n\n\n\n
= 8 + 4 + 0 + 1 = 13_{10}
]<\/p>\n\n\n\nStep 2: Convert the fractional part (0.0110) to decimal<\/strong><\/h3>\n\n\n\n
[
0.0110_2 = (0 \u00d7 2^{-1}) + (1 \u00d7 2^{-2}) + (1 \u00d7 2^{-3}) + (0 \u00d7 2^{-4})
]<\/p>\n\n\n\n
= (0 \u00d7 0.5) + (1 \u00d7 0.25) + (1 \u00d7 0.125) + (0 \u00d7 0.0625)
]<\/p>\n\n\n\n
= 0 + 0.25 + 0.125 + 0
]<\/p>\n\n\n\n
= 0.375_{10}
]<\/p>\n\n\n\nStep 3: Add both parts<\/strong><\/h3>\n\n\n\n
13 + 0.375 = 13.375_{10}
]<\/p>\n\n\n\n
\n\n\n\nExplanation (300 Words)<\/strong><\/h3>\n\n\n\n