Let’s first convert the binary numbers to decimal<\/strong> and hexadecimal<\/strong>.<\/p>\n\n\n\n We split the binary number into its integer<\/strong> and fractional<\/strong> parts:<\/p>\n\n\n\n Decimal Result:<\/strong> 1+0.5625=1.56251 + 0.5625 = 1.5625<\/p>\n\n\n\n Group the binary digits from the point outward:<\/p>\n\n\n\n Hexadecimal Result:<\/strong> 1.9161.9_{16}<\/p>\n\n\n\n Decimal Result:<\/strong> 6+0.25=6.256 + 0.25 = 6.25<\/p>\n\n\n\n Hexadecimal Result:<\/strong> 6.4166.4_{16}<\/p>\n\n\n\n From the decimal results:<\/p>\n\n\n\n This happens because of the structure of binary numbers.<\/p>\n\n\n\n Let\u2019s analyze:<\/p>\n\n\n\n If we shift all bits<\/strong> of (a) left by two places<\/strong> (i.e., multiply by 22=42^2 = 4), we get:<\/p>\n\n\n\n This is the exact value of (b). So, shifting left by 2 bits (which multiplies by 4 in binary) shows that (b) is 4 times (a).<\/p>\n\n\n\n Conclusion:<\/strong> In binary, each left shift by one bit multiplies the number by 2. Shifting 1.10010 left two places gives 110.010, thus explaining why (b) = 4 \u00d7 (a).<\/p>\n\n\n\n Convert the following binary numbers to hexadecimal and decimal: (a) 1.10010, (b) 110.010. Explain why the decimal answer in (b) is 4 times that in (a). The Correct Answer and Explanation is: Let’s first convert the binary numbers to decimal and hexadecimal. (a) Binary: 1.10010 Decimal Conversion: We split the binary number into its integer […]<\/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-225324","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225324","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=225324"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225324\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225324"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225324"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225324"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n(a) Binary: 1.10010<\/strong><\/h3>\n\n\n\n
Decimal Conversion:<\/h4>\n\n\n\n
\n
1<\/code> = 1\u00d720=11 \\times 2^0 = 1<\/li>\n\n\n\n.10010<\/code>
=1\u00d72\u22121+0\u00d72\u22122+0\u00d72\u22123+1\u00d72\u22124+0\u00d72\u22125= 1 \\times 2^{-1} + 0 \\times 2^{-2} + 0 \\times 2^{-3} + 1 \\times 2^{-4} + 0 \\times 2^{-5}
=0.5+0+0+0.0625+0= 0.5 + 0 + 0 + 0.0625 + 0
=0.5625= 0.5625<\/li>\n<\/ul>\n\n\n\nHexadecimal Conversion:<\/h4>\n\n\n\n
\n
1.10010<\/code> \u2192 Pad to 4 bits after and before the point: 0001.1001 0000<\/code>
\u2192 Integer part: 0001<\/code> = 1
\u2192 Fractional part: 1001<\/code> = 9 (Hex)
\u2192 (Next digit 0000<\/code> = 0, but not significant beyond 4 bits)<\/li>\n<\/ul>\n\n\n\n
\n\n\n\n(b) Binary: 110.010<\/strong><\/h3>\n\n\n\n
Decimal Conversion:<\/h4>\n\n\n\n
\n
110<\/code> = 1\u00d722+1\u00d721+0\u00d720=4+2+0=61 \\times 2^2 + 1 \\times 2^1 + 0 \\times 2^0 = 4 + 2 + 0 = 6<\/li>\n\n\n\n.010<\/code>
=0\u00d72\u22121+1\u00d72\u22122+0\u00d72\u22123=0+0.25+0=0.25= 0 \\times 2^{-1} + 1 \\times 2^{-2} + 0 \\times 2^{-3} = 0 + 0.25 + 0 = 0.25<\/li>\n<\/ul>\n\n\n\nHexadecimal Conversion:<\/h4>\n\n\n\n
\n
110.010<\/code> \u2192 Pad to: 0110.0100<\/code>
\u2192 Integer part: 0110<\/code> = 6
\u2192 Fractional part: 0100<\/code> = 4<\/li>\n<\/ul>\n\n\n\n
\n\n\n\nWhy is (b) 4 times (a)?<\/h3>\n\n\n\n
\n
\n
1.10010<\/code><\/li>\n\n\n\n110.010<\/code><\/li>\n<\/ul>\n\n\n\n1.10010 \u00d7 2^2 = 110.010\n<\/code><\/pre>\n\n\n\n![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner7-157.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"