Convert the following numbers to their equivalent decimal values. <\/p>\n\n\n\n
a. 11001012 b. 10011011001.101102 c. B2F16 d. 011010010111BCD e. 3748<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n Let’s go through each conversion step by step.<\/p>\n\n\n\n To convert the binary number 110010121100101_2 to decimal, we assign powers of 2 to each digit from right to left: 11001012=(1\u00d726)+(1\u00d725)+(0\u00d724)+(0\u00d723)+(1\u00d722)+(0\u00d721)+(1\u00d720)1100101_2 = (1 \\times 2^6) + (1 \\times 2^5) + (0 \\times 2^4) + (0 \\times 2^3) + (1 \\times 2^2) + (0 \\times 2^1) + (1 \\times 2^0)<\/p>\n\n\n\n Calculating each term: =(1\u00d764)+(1\u00d732)+(0\u00d716)+(0\u00d78)+(1\u00d74)+(0\u00d72)+(1\u00d71)= (1 \\times 64) + (1 \\times 32) + (0 \\times 16) + (0 \\times 8) + (1 \\times 4) + (0 \\times 2) + (1 \\times 1) =64+32+0+0+4+0+1=101= 64 + 32 + 0 + 0 + 4 + 0 + 1 = 101<\/p>\n\n\n\n So, 11001012=101101100101_2 = 101_{10}.<\/p>\n\n\n\n The integer part is 10011011001210011011001_2, and the fractional part is 101121011_2.<\/p>\n\n\n\n Integer part:<\/strong> 100110110012=(1\u00d7210)+(0\u00d729)+(0\u00d728)+(1\u00d727)+(1\u00d726)+(0\u00d725)+(1\u00d724)+(1\u00d723)+(0\u00d722)+(0\u00d721)+(1\u00d720)10011011001_2 = (1 \\times 2^{10}) + (0 \\times 2^9) + (0 \\times 2^8) + (1 \\times 2^7) + (1 \\times 2^6) + (0 \\times 2^5) + (1 \\times 2^4) + (1 \\times 2^3) + (0 \\times 2^2) + (0 \\times 2^1) + (1 \\times 2^0) =1024+0+0+128+64+0+16+8+0+0+1=1241= 1024 + 0 + 0 + 128 + 64 + 0 + 16 + 8 + 0 + 0 + 1 = 1241<\/p>\n\n\n\n Fractional part:<\/strong> .10112=(1\u00d72\u22121)+(0\u00d72\u22122)+(1\u00d72\u22123)+(1\u00d72\u22124).1011_2 = (1 \\times 2^{-1}) + (0 \\times 2^{-2}) + (1 \\times 2^{-3}) + (1 \\times 2^{-4}) =0.5+0+0.125+0.0625=0.6875= 0.5 + 0 + 0.125 + 0.0625 = 0.6875<\/p>\n\n\n\n So, 10011011001.10112=1241.68751010011011001.1011_2 = 1241.6875_{10}.<\/p>\n\n\n\n Hexadecimal uses base 16. The number B2F16B2F_{16} can be expanded as follows: B2F16=(B\u00d7162)+(2\u00d7161)+(F\u00d7160)B2F_{16} = (B \\times 16^2) + (2 \\times 16^1) + (F \\times 16^0)<\/p>\n\n\n\n Where B=11B = 11 and F=15F = 15: =(11\u00d7256)+(2\u00d716)+(15\u00d71)= (11 \\times 256) + (2 \\times 16) + (15 \\times 1) =2816+32+15=2863= 2816 + 32 + 15 = 2863<\/p>\n\n\n\n So, B2F16=286310B2F_{16} = 2863_{10}.<\/p>\n\n\n\n This looks like a mix of binary and hexadecimal digits. Let’s first consider only the binary part and convert it.<\/p>\n\n\n\n The binary part is 0110100101112011010010111_2: 0110100101112=(0\u00d7211)+(1\u00d7210)+(1\u00d729)+(0\u00d728)+(1\u00d727)+(0\u00d726)+(0\u00d725)+(1\u00d724)+(0\u00d723)+(1\u00d722)+(1\u00d721)+(1\u00d720)011010010111_2 = (0 \\times 2^{11}) + (1 \\times 2^{10}) + (1 \\times 2^9) + (0 \\times 2^8) + (1 \\times 2^7) + (0 \\times 2^6) + (0 \\times 2^5) + (1 \\times 2^4) + (0 \\times 2^3) + (1 \\times 2^2) + (1 \\times 2^1) + (1 \\times 2^0) =0+1024+512+0+128+0+0+16+0+4+2+1=1687= 0 + 1024 + 512 + 0 + 128 + 0 + 0 + 16 + 0 + 4 + 2 + 1 = 1687<\/p>\n\n\n\n For the hexadecimal part BCDBCD, let’s convert it to decimal. BCD16=(B\u00d7162)+(C\u00d7161)+(D\u00d7160)BCD_{16} = (B \\times 16^2) + (C \\times 16^1) + (D \\times 16^0)<\/p>\n\n\n\n Where B=11B = 11, C=12C = 12, and D=13D = 13: =(11\u00d7256)+(12\u00d716)+(13\u00d71)= (11 \\times 256) + (12 \\times 16) + (13 \\times 1) =2816+192+13=3021= 2816 + 192 + 13 = 3021<\/p>\n\n\n\n Thus, the total value is: 1687+3021=47081687 + 3021 = 4708<\/p>\n\n\n\n So, 011010010111BCD16=470810011010010111BCD_{16} = 4708_{10}.<\/p>\n\n\n\n The number 37483748 is already in decimal, so it remains as 3748103748_{10}.<\/p>\n\n\n\n a. 11001012=101101100101_2 = 101_{10} Convert the following numbers to their equivalent decimal values. a. 11001012 b. 10011011001.101102 c. B2F16 d. 011010010111BCD e. 3748 The correct answer and explanation is: Let’s go through each conversion step by step. a. 1100101\u2082 (Binary to Decimal) To convert the binary number 110010121100101_2 to decimal, we assign powers of 2 to each digit from […]<\/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-252536","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252536","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=252536"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252536\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=252536"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=252536"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=252536"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}a. 1100101\u2082<\/strong> (Binary to Decimal)<\/h3>\n\n\n\n
\n\n\n\nb. 10011011001.1011\u2082<\/strong> (Binary to Decimal)<\/h3>\n\n\n\n
\n\n\n\nc. B2F\u2081\u2086<\/strong> (Hexadecimal to Decimal)<\/h3>\n\n\n\n
\n\n\n\nd. 011010010111BCD<\/strong> (Mixed Base to Decimal)<\/h3>\n\n\n\n
\n\n\n\ne. 3748<\/strong> (Decimal to Decimal)<\/h3>\n\n\n\n
\n\n\n\nSummary of Answers:<\/h3>\n\n\n\n
b. 10011011001.10112=1241.68751010011011001.1011_2 = 1241.6875_{10}
c. B2F16=286310B2F_{16} = 2863_{10}
d. 011010010111BCD16=470810011010010111BCD_{16} = 4708_{10}
e. 374810=3748103748_{10} = 3748_{10}<\/p>\n","protected":false},"excerpt":{"rendered":"