Correct Answers:<\/strong><\/p>\n\n\n\n (a) Conversions<\/strong><\/p>\n\n\n\n (i)<\/strong> Convert 11000211000_2110002\u200b to decimal: (ii)<\/strong> Convert 25.1251025.125_{10}25.12510\u200b to binary:<\/p>\n\n\n\n (iii)<\/strong> Convert 4B.3164B.3_{16}4B.316\u200b to binary:<\/p>\n\n\n\n (b) Representing -52 in 8-bit binary<\/strong><\/p>\n\n\n\n First, find binary of 525252: (i) Signed Magnitude Form<\/strong> (ii) 2’s Complement Form<\/strong> Explanation :<\/strong><\/p>\n\n\n\n Binary, decimal, and hexadecimal number systems represent numerical values in different bases. To convert between them, understanding place values is essential. The binary number 11000211000_2110002\u200b is in base two, meaning each digit represents powers of two from right to left. Evaluating each digit’s weight gives the decimal equivalent, which is 24.<\/p>\n\n\n\n For converting a decimal with a fractional part like 25.125 to binary, handle the integer and fractional parts separately. The integer 25 converts directly to binary by successive division by two, giving 11001. For the fractional part, multiply it repeatedly by two and extract the integer part at each step. This method, applied to 0.125, produces the binary fraction 0.001. Combining both gives 11001.001.<\/p>\n\n\n\n Converting hexadecimal to binary is straightforward. Each hexadecimal digit maps to a 4-bit binary value. Thus, 4 becomes 0100, B becomes 1011, and the fractional 3 maps to 0011. Joining them yields 01001011.0011.<\/p>\n\n\n\n Representing negative numbers in binary involves using fixed formats. The signed magnitude method uses the first bit for the sign (1 for negative) and the remaining for the magnitude. Therefore, -52 becomes 10110100.<\/p>\n\n\n\n The two’s complement method is more commonly used in computing. It simplifies binary arithmetic, especially for subtraction. To find the two’s complement, first invert all bits of the positive number and then add one to the result. Applying this to 52 (00110100) results in 11001100, the correct 8-bit representation of -52 in two’s complement.<\/p>\n\n\n\n Each of these binary techniques is crucial in computer systems for data representation, computation, and storage.<\/p>\n\n\n\n Convert 11000(2) into a decimal number. (ii) Convert 25.125(10) into a binary number. (iii) Convert 4B.3(16) into a binary number. (b) Express -52 in to an 8-bit (i) signed magnitude form and (ii) 2’s complement form. The Correct Answer and Explanation is: Correct Answers: (a) Conversions (i) Convert 11000211000_2110002\u200b to decimal:110002=1\u00d724+1\u00d723+0\u00d722+0\u00d721+0\u00d720=16+8+0+0+0=241011000_2 = 1\u00d72^4 + 1\u00d72^3 + 0\u00d72^2 + 0\u00d72^1 + 0\u00d72^0 […]<\/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-236689","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236689","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=236689"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236689\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=236689"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=236689"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=236689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
110002=1\u00d724+1\u00d723+0\u00d722+0\u00d721+0\u00d720=16+8+0+0+0=241011000_2 = 1\u00d72^4 + 1\u00d72^3 + 0\u00d72^2 + 0\u00d72^1 + 0\u00d72^0 = 16 + 8 + 0 + 0 + 0 = \\boxed{24_{10}}110002\u200b=1\u00d724+1\u00d723+0\u00d722+0\u00d721+0\u00d720=16+8+0+0+0=2410\u200b\u200b<\/p>\n\n\n\n\n
\u20030.125 \u00d7 2 = 0.25 \u2192 0
\u20030.25 \u00d7 2 = 0.5 \u2192 0
\u20030.5 \u00d7 2 = 1.0 \u2192 1
So, 0.12510=0.00120.125_{10} = 0.001_20.12510\u200b=0.0012\u200b
Hence, 25.12510=11001.001225.125_{10} = \\boxed{11001.001_2}25.12510\u200b=11001.0012\u200b\u200b<\/li>\n<\/ul>\n\n\n\n\n
\n\n\n\n
5210=00110100252_{10} = 00110100_25210\u200b=001101002\u200b<\/p>\n\n\n\n
Keep magnitude bits same: 001101000011010000110100
Sign bit is 1 (negative), so:
10110100\\boxed{10110100}10110100\u200b<\/p>\n\n\n\n
Start with +52=00110100+52 = 00110100+52=00110100
First, invert bits: 110010111100101111001011
Then, add 1:
\u2003\u200311001011
+\u2003\u2003\u2003\u2003\u200301
=\u2003\u2003\\boxed{11001100}<\/p>\n\n\n\n
\n\n\n\n![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-707.jpeg\")
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