. 1010 1011<\/strong><\/p>\n\n\n\n Decimal Conversion:<\/strong> So, for 1010 1011: 10101011=(1\u00d727)+(0\u00d726)+(1\u00d725)+(0\u00d724)+(1\u00d723)+(0\u00d722)+(1\u00d721)+(1\u00d720)1010 1011 = (1 \\times 2^7) + (0 \\times 2^6) + (1 \\times 2^5) + (0 \\times 2^4) + (1 \\times 2^3) + (0 \\times 2^2) + (1 \\times 2^1) + (1 \\times 2^0)10101011=(1\u00d727)+(0\u00d726)+(1\u00d725)+(0\u00d724)+(1\u00d723)+(0\u00d722)+(1\u00d721)+(1\u00d720) =128+0+32+0+8+0+2+1= 128 + 0 + 32 + 0 + 8 + 0 + 2 + 1=128+0+32+0+8+0+2+1 =171= 171=171<\/p>\n\n\n\n Hexadecimal Conversion:<\/strong> So, the hexadecimal representation is AB<\/strong>.<\/p>\n\n\n\n b. 0011 0001<\/strong><\/p>\n\n\n\n Decimal Conversion:<\/strong> Hexadecimal Conversion:<\/strong> 00110001\u21920011=3and0001=10011 0001 \\rightarrow 0011 = 3 \\quad \\text{and} \\quad 0001 = 100110001\u21920011=3and0001=1<\/p>\n\n\n\n So, the hexadecimal representation is 31<\/strong>.<\/p>\n\n\n\n c. 1110 0111<\/strong><\/p>\n\n\n\n Decimal Conversion:<\/strong> Hexadecimal Conversion:<\/strong> 11100111\u21921110=Eand0111=71110 0111 \\rightarrow 1110 = E \\quad \\text{and} \\quad 0111 = 711100111\u21921110=Eand0111=7<\/p>\n\n\n\n So, the hexadecimal representation is E7<\/strong>.<\/p>\n\n\n\n d. 1111 1111<\/strong><\/p>\n\n\n\n Decimal Conversion:<\/strong> Hexadecimal Conversion:<\/strong> 11111111\u21921111=Fand1111=F1111 1111 \\rightarrow 1111 = F \\quad \\text{and} \\quad 1111 = F11111111\u21921111=Fand1111=F<\/p>\n\n\n\n So, the hexadecimal representation is FF<\/strong>.<\/p>\n\n\n\n Summary of results:<\/strong><\/p>\n\n\n\n I hope this breakdown helps you understand the conversion process! Let me know if you’d like to explore more examples.<\/p>\n\n\n\n Convert from binary to decimal to hexadecimal (PLEASE SHOW ALL WORK) a. 1010 1011 – decimal: – hexadecimal b. 0011 0001 – decimal: – hexadecimal: c. 1110 0111 – decimal: – hexadecimal: d. 1111 1111 – decimal: – hexadecimal: The Correct Answer and Explanation is: . 1010 1011 Decimal Conversion:To convert a binary number to […]<\/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-254147","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/254147","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=254147"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/254147\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=254147"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=254147"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=254147"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
To convert a binary number to decimal, we multiply each bit by 2 raised to the power of its position (starting from 0 at the far right).<\/p>\n\n\n\n
To convert a binary number to hexadecimal, group the binary digits in sets of four (starting from the right), and then convert each set to its hexadecimal equivalent. 10101011\u21921010=Aand1011=B1010 1011 \\rightarrow 1010 = A \\quad \\text{and} \\quad 1011 = B10101011\u21921010=Aand1011=B<\/p>\n\n\n\n
\n\n\n\n
For 0011 0001: 00110001=(0\u00d727)+(0\u00d726)+(1\u00d725)+(1\u00d724)+(0\u00d723)+(0\u00d722)+(0\u00d721)+(1\u00d720)0011 0001 = (0 \\times 2^7) + (0 \\times 2^6) + (1 \\times 2^5) + (1 \\times 2^4) + (0 \\times 2^3) + (0 \\times 2^2) + (0 \\times 2^1) + (1 \\times 2^0)00110001=(0\u00d727)+(0\u00d726)+(1\u00d725)+(1\u00d724)+(0\u00d723)+(0\u00d722)+(0\u00d721)+(1\u00d720) =0+0+32+16+0+0+0+1= 0 + 0 + 32 + 16 + 0 + 0 + 0 + 1=0+0+32+16+0+0+0+1 =49= 49=49<\/p>\n\n\n\n
\n\n\n\n
For 1110 0111: 11100111=(1\u00d727)+(1\u00d726)+(1\u00d725)+(0\u00d724)+(0\u00d723)+(1\u00d722)+(1\u00d721)+(1\u00d720)1110 0111 = (1 \\times 2^7) + (1 \\times 2^6) + (1 \\times 2^5) + (0 \\times 2^4) + (0 \\times 2^3) + (1 \\times 2^2) + (1 \\times 2^1) + (1 \\times 2^0)11100111=(1\u00d727)+(1\u00d726)+(1\u00d725)+(0\u00d724)+(0\u00d723)+(1\u00d722)+(1\u00d721)+(1\u00d720) =128+64+32+0+0+4+2+1= 128 + 64 + 32 + 0 + 0 + 4 + 2 + 1=128+64+32+0+0+4+2+1 =231= 231=231<\/p>\n\n\n\n
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For 1111 1111: 11111111=(1\u00d727)+(1\u00d726)+(1\u00d725)+(1\u00d724)+(1\u00d723)+(1\u00d722)+(1\u00d721)+(1\u00d720)1111 1111 = (1 \\times 2^7) + (1 \\times 2^6) + (1 \\times 2^5) + (1 \\times 2^4) + (1 \\times 2^3) + (1 \\times 2^2) + (1 \\times 2^1) + (1 \\times 2^0)11111111=(1\u00d727)+(1\u00d726)+(1\u00d725)+(1\u00d724)+(1\u00d723)+(1\u00d722)+(1\u00d721)+(1\u00d720) =128+64+32+16+8+4+2+1= 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1=128+64+32+16+8+4+2+1 =255= 255=255<\/p>\n\n\n\n
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