{"id":188731,"date":"2025-02-07T08:48:12","date_gmt":"2025-02-07T08:48:12","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=188731"},"modified":"2025-02-07T08:48:14","modified_gmt":"2025-02-07T08:48:14","slug":"realize-the-code-converter-which-converts-the-binary-bcd-code-into-the-hamming-code-as-specified","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/07\/realize-the-code-converter-which-converts-the-binary-bcd-code-into-the-hamming-code-as-specified\/","title":{"rendered":"Realize the code converter which converts the binary (BCD) code into the Hamming code as specified"},"content":{"rendered":"\n

Realize the code converter which converts the binary (BCD) code into the Hamming code as specified in Table 6.4.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

onverting Binary-Coded Decimal (BCD) to Hamming code involves encoding each decimal digit, represented in BCD, into a Hamming codeword.CD represents each decimal digit with a 4-bit binary number, while Hamming codes are error-correcting codes that add redundancy to detect and correct errors in data transmission.
Understanding BCD:<\/strong>
CD encodes each decimal digit (0-9) as a 4-bit binary number.For example:
Decimal 0: 0000- Decimal 1: 0001- Decimal 2: 0010- Decimal 3: 0011- Decimal 4: 0100- Decimal 5: 0101- Decimal 6: 0110- Decimal 7: 0111- Decimal 8: 1000- Decimal 9: 1001
Understanding Hamming Code:<\/strong>
amming codes are error-correcting codes that add parity bits to data bits to detect and correct single-bit errors.or a 4-bit data input, a 7-bit Hamming code is commonly used, which includes 3 parity bits.he positions of the parity bits are powers of two (1, 2, and 4), and the data bits occupy the remaining positions.
Converting BCD to Hamming Code:<\/strong>
o convert a 4-bit BCD digit to a 7-bit Hamming code:. Identify Data and Parity Bits:<\/strong> – Data bits (D): Positions 3, 5, 6, and 7 – Parity bits (P): Positions 1, 2, and 4. Assign Data Bits:<\/strong> Place the 4 BCD bits into the data bit positions.. Calculate Parity Bits:<\/strong> – P1<\/strong> covers positions 1, 3, 5, and 7. Set P1 to 1 if the number of 1s in these positions is odd; otherwise, set it to 0. – P2<\/strong> covers positions 2, 3, 6, and 7. Set P2 to 1 if the number of 1s in these positions is odd; otherwise, set it to 0. – P4<\/strong> covers positions 4, 5, 6, and 7. Set P4 to 1 if the number of 1s in these positions is odd; otherwise, set it to 0.. Construct the Hamming Code:<\/strong> Combine the parity bits and data bits to form the 7-bit Hamming codeword.
Example:<\/strong>
onsider the BCD digit for decimal 5, which is 0101.. Assign Data Bits:<\/strong> – D1 = 0 – D2 = 1 – D3 = 0 – D4 = 1. Calculate Parity Bits:<\/strong> – P1<\/strong> covers positions 1, 3, 5, and 7: P1 = 0 (even number of 1s) – P2<\/strong> covers positions 2, 3, 6, and 7: P2 = 1 (odd number of 1s) – P4<\/strong> covers positions 4, 5, 6, and 7: P4 = 0 (even number of 1s). Construct the Hamming Code:<\/strong> – Hamming codeword: P1 P2 D1 P4 D2 D3 D4 – Hamming codeword: 0 1 0 0 1 0 1
herefore, the 7-bit Hamming code for the BCD digit 0101 (decimal 5) is 0100101.
his process ensures that each 4-bit BCD digit is represented by a 7-bit Hamming code, allowing for error detection and correction in data transmission.
For a visual demonstration of constructing a Hamming code for a BCD digit, you can refer to the following video:<\/p>\n\n\n\n

\ue200video\ue202Construction of Hamming Code for BCD 0110\ue202turn0search6\ue201<\/p>\n","protected":false},"excerpt":{"rendered":"

Realize the code converter which converts the binary (BCD) code into the Hamming code as specified in Table 6.4. The Correct Answer and Explanation is : onverting Binary-Coded Decimal (BCD) to Hamming code involves encoding each decimal digit, represented in BCD, into a Hamming codeword.CD represents each decimal digit with a 4-bit binary number, while […]<\/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-188731","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188731","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=188731"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188731\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=188731"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=188731"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=188731"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}