How many bits are required to represent the decimal numbers in the range from 0 to 999 using <\/p>\n\n\n\n
(a) straight binary code? <\/p>\n\n\n\n
(b) Using BCD code?<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n To represent decimal numbers from 0 to 999<\/strong>, we analyze both straight binary<\/strong> and BCD (Binary-Coded Decimal)<\/strong>.<\/p>\n\n\n\n We need the minimum number of bits N<\/strong> such that:<\/p>\n\n\n\n $$ Let\u2019s calculate:<\/p>\n\n\n\n So, we need 10 bits<\/strong>.<\/p>\n\n\n\n \u2705 Answer: 10 bits<\/strong><\/p>\n\n\n\n BCD represents each decimal digit<\/strong> using 4 bits<\/strong>. Since 999 has 3 digits (hundreds, tens, units), we need:<\/p>\n\n\n\n $$ \u2705 Answer: 12 bits<\/strong><\/p>\n\n\n\n When representing numbers digitally, the efficiency of representation depends on the coding method. For the decimal range 0 to 999, two common methods are straight binary<\/strong> and BCD<\/strong>.<\/p>\n\n\n\n Straight binary<\/strong> uses a base-2 positional system. Each bit can be 0 or 1, and the value is calculated as powers of 2. To determine how many bits are needed, we find the smallest power of 2 greater than 999. As calculated above, $2^10 = 1024$ is the first power greater than 999, so 10 bits<\/strong> are sufficient to represent all numbers from 0 to 999. This approach is compact and efficient in terms of bit usage.<\/p>\n\n\n\n BCD (Binary-Coded Decimal)<\/strong>, on the other hand, encodes each individual decimal digit separately using 4 bits. For example, the number 345 in BCD is represented as:<\/p>\n\n\n\n For numbers up to 999, which have 3 digits, BCD always uses 3 \u00d7 4 = 12 bits<\/strong>, regardless of the actual numeric value. BCD is easier for digital displays and human-readable formats but is less efficient<\/strong> than straight binary for storing pure numeric data because it wastes bit patterns that don\u2019t correspond to decimal digits (e.g., 1010 to 1111 are unused in each 4-bit digit).<\/p>\n\n\n\n In conclusion, straight binary requires only 10 bits<\/strong>, whereas BCD requires 12 bits<\/strong> for the same range, trading storage efficiency for simplicity in decimal digit handling.<\/p>\n","protected":false},"excerpt":{"rendered":" How many bits are required to represent the decimal numbers in the range from 0 to 999 using (a) straight binary code? (b) Using BCD code? The correct answer and explanation is : To represent decimal numbers from 0 to 999, we analyze both straight binary and BCD (Binary-Coded Decimal). \u2705 (a) Straight Binary Code: […]<\/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-212003","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/212003","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=212003"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/212003\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=212003"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=212003"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=212003"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n\u2705 (a) Straight Binary Code:<\/strong><\/h3>\n\n\n\n
2^N > 999
$$<\/p>\n\n\n\n\n
\n\n\n\n\u2705 (b) BCD Code:<\/strong><\/h3>\n\n\n\n
3 \\text{ digits} \\times 4 \\text{ bits per digit} = 12 \\text{ bits}
$$<\/p>\n\n\n\n
\n\n\n\n\u270d\ufe0f Explanation (Approx. 300 Words):<\/h3>\n\n\n\n
\n
So, 345 \u2192 0011 0100 0101 (12 bits total)<\/li>\n<\/ul>\n\n\n\n