{"id":29,"date":"2020-08-29T02:52:38","date_gmt":"2020-08-29T02:52:38","guid":{"rendered":"http:\/\/learnlearn.uk\/igcsecs\/?page_id=29"},"modified":"2023-11-01T17:48:48","modified_gmt":"2023-11-01T17:48:48","slug":"error-detection","status":"publish","type":"page","link":"https:\/\/learnlearn.uk\/igcsecs\/error-detection\/","title":{"rendered":"Error Detection &#8211; Parity Bits, Check Digits &#038; Check Sums"},"content":{"rendered":"<div class=\"responsive-tabs\">\n<h2 class=\"tabtitle\">Introduction<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Why do errors occur?<\/h3>\n<p>When data is transferred through a network at each stage there is possibility that data might get corrupted. Therefore when a packet is received it needs to be checked to ensure the integrity of the data. Two common ways this can be achieved is through the use of\u00a0<strong>parity bits<\/strong>\u00a0and\u00a0<strong>check-sums<\/strong>.<\/p>\n<p>&nbsp;<\/p>\n\n<\/div><h2 class=\"tabtitle\">Parity Bit<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Parity Bit (Aka Check Bit)<\/h3>\n<p>A check bit is a simple method of error checking used to <strong>detect data corruption\u00a0of small blocks of data <\/strong>(usually at byte level)\u00a0during storage or transmission of data. A single bit of data is added to a string of bits and order to ensure that the sum of the total of bits is either even or odd.<\/p>\n<ul>\n<li>If <strong>even parity<\/strong> is used then sum of the digits must add up to an even number<\/li>\n<li>If<strong> odd parity<\/strong> is used the sum of the digits must add up to an off number<\/li>\n<\/ul>\n<p>After the data is transmitted, the receiving device adds up the string of bits again (this time including the added bits) and checks it for parity.<\/p>\n<p>If the received data does not match the required parity then the data is corrupt and must be re-sent.<\/p>\n<p><strong>Example(using even parity)<\/strong><\/p>\n<table style=\"height: 120px;\" width=\"829\">\n<tbody>\n<tr>\n<td><span style=\"font-weight: 400;\">Original 7-bit binary data<\/span><\/td>\n<td><span style=\"font-weight: 400;\">0110101<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Binary data with 0 parity bit added\u00a0<\/span><\/td>\n<td><span style=\"font-weight: 400;\">0110101<\/span><span style=\"font-weight: 400;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">Example received data (corrupted)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">01<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">01010\u00a0 \u00a0 (Now odd number of 1s)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>In the example above the 7 original bits added up to an even number, so a 0 was added to the end. When the data was received the number now added up to an odd number, so the data must have been corrupted during the transmission process.<\/p>\n<p><strong>Limitations of parity bits<\/strong><\/p>\n<p>A parity bit check is not perfect and some errors are still possible (for example if 2 bits have been corrupted)<\/p>\n\n<\/div><h2 class=\"tabtitle\">Check Digits<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Check Digits<\/h3>\n<p>A check digit is a single digit number that is added to the end of a string of digits to <strong>detect human error<\/strong> during manual entry, such as entering a wrong digit or reversing two digits when entering a credit card on a shopping website.<\/p>\n<p>Check digits are commonly used on:<\/p>\n<ul>\n<li>Barcodes<\/li>\n<li>Credit Cards<\/li>\n<li>Account Numbers<\/li>\n<li>Government ID Numbers<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<div id=\"attachment_380\" style=\"width: 310px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/learnlearn.uk\/igcsecs\/wp-content\/uploads\/sites\/23\/2020\/08\/ISBN-13.jpg\"><img aria-describedby=\"caption-attachment-380\" decoding=\"async\" loading=\"lazy\" class=\"wp-image-380 size-full\" src=\"https:\/\/learnlearn.uk\/igcsecs\/wp-content\/uploads\/sites\/23\/2020\/08\/ISBN-13.jpg\" alt=\"\" width=\"300\" height=\"150\" \/><\/a><p id=\"caption-attachment-380\" class=\"wp-caption-text\">Check digits can be found everywhere, from food packaging to the barcode on the back of your favourite book.<\/p><\/div>\n\n<\/div><h2 class=\"tabtitle\">Luhn's Algorithm<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Luhn&#8217;s Algorithm<\/h3>\n<p>Luhn&#8217;s algorithm is a simple mathematical technique that used modulo to detect simple errors. It is commonly used on 15 digit credit card numbers to automatically calculate the 16th digit.<\/p>\n<p>The technique is simple.<\/p>\n<p>Write all the digits down in order.<\/p>\n<ol>\n<li>For each number in the sequence that is in an odd position (first, third, fifth,etc) multiply that number by two and add each of the digits of the result together.<\/li>\n<li>For each number in the sequence that is\u00a0 in even position, leave it as is.<\/li>\n<li>Now add up all the resultant numbers together (including the ones you left as is)<\/li>\n<li>Work out 10 minus modulo 10 of the total\u00a0 ( = 10 &#8211; Total MOD 10 )<\/li>\n<li>The answer is the 16th digit!<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/docs.google.com\/presentation\/d\/e\/2PACX-1vR3TnvSqxKNb_Y9uwqCR4ULA_ihmYpWq1q_R6wA0yNIJRTcljQLHxChpNH5qQ73PA8L8M6u2638xmBA\/embed?start=false&amp;loop=true&amp;delayms=3000\" width=\"960\" height=\"569\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div>If you want to try it out live, <a href=\"https:\/\/docs.google.com\/spreadsheets\/d\/1tVJmH1e-vtEpXetUvYzLXgrBAAc9S7eB9oj_9UvXIxs\/edit?usp=sharing\">Try out it on this google sheets doc<\/a> (Go To File &gt; Make a copy) and use your own numbers<\/div>\n<div><\/div>\n<div id=\"attachment_381\" style=\"width: 310px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/learnlearn.uk\/igcsecs\/wp-content\/uploads\/sites\/23\/2020\/08\/credit-card-4438385_1280.png\"><img aria-describedby=\"caption-attachment-381\" decoding=\"async\" loading=\"lazy\" class=\"wp-image-381 size-medium\" src=\"https:\/\/learnlearn.uk\/igcsecs\/wp-content\/uploads\/sites\/23\/2020\/08\/credit-card-4438385_1280-300x212.png\" alt=\"\" width=\"300\" height=\"212\" srcset=\"https:\/\/learnlearn.uk\/igcsecs\/wp-content\/uploads\/sites\/23\/2020\/08\/credit-card-4438385_1280-300x212.png 300w, https:\/\/learnlearn.uk\/igcsecs\/wp-content\/uploads\/sites\/23\/2020\/08\/credit-card-4438385_1280-768x543.png 768w, https:\/\/learnlearn.uk\/igcsecs\/wp-content\/uploads\/sites\/23\/2020\/08\/credit-card-4438385_1280-1024x724.png 1024w, https:\/\/learnlearn.uk\/igcsecs\/wp-content\/uploads\/sites\/23\/2020\/08\/credit-card-4438385_1280.png 1280w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><p id=\"caption-attachment-381\" class=\"wp-caption-text\">Is this a valid card number? Trying working out the answer by using Luhn&#8217;s algorithm below<\/p><\/div>\n<h3><\/h3>\n<p>&nbsp;<\/p>\n<p>Barcodes use a mod 10 algorithm with a 3x multiplier instead of a 2x<\/p>\n\n<\/div><h2 class=\"tabtitle\">Check sums<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Check Sums<\/h3>\n<p>Check sums are used to <strong>detect accidental corruption of large blocks of data<\/strong> after transmission of storage. They are commonly used to verify the integrity of downloaded files or programs after downloading them from the internet.<\/p>\n<p>The use more complex algorithms than check digits or parity bits and the resultant sum is much larger in size. While checksums do not 100% guarantee the integrity of data ensure a very high probability of corruption detection.<\/p>\n<p><a href=\"https:\/\/learnlearn.uk\/igcsecs\/wp-content\/uploads\/sites\/23\/2020\/08\/checksum-example.png\"><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-382 \" src=\"https:\/\/learnlearn.uk\/igcsecs\/wp-content\/uploads\/sites\/23\/2020\/08\/checksum-example.png?_t=1642039585\" alt=\"\" width=\"645\" height=\"641\" srcset=\"https:\/\/learnlearn.uk\/igcsecs\/wp-content\/uploads\/sites\/23\/2020\/08\/checksum-example.png 1024w, https:\/\/learnlearn.uk\/igcsecs\/wp-content\/uploads\/sites\/23\/2020\/08\/checksum-example-150x150.png 150w, https:\/\/learnlearn.uk\/igcsecs\/wp-content\/uploads\/sites\/23\/2020\/08\/checksum-example-300x298.png 300w, https:\/\/learnlearn.uk\/igcsecs\/wp-content\/uploads\/sites\/23\/2020\/08\/checksum-example-768x763.png 768w\" sizes=\"(max-width: 645px) 100vw, 645px\" \/><\/a><\/p>\n<h3><\/h3>\n\n<\/div><h2 class=\"tabtitle\">Resources<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Resources<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=jLuj62Gq-1I\">Parity Bits tutorial<\/a><\/p>\n<p><a href=\"https:\/\/docs.google.com\/spreadsheets\/d\/1tVJmH1e-vtEpXetUvYzLXgrBAAc9S7eB9oj_9UvXIxs\/edit?usp=sharing\">Luhn&#8217;s Algorithm Google Sheet<\/a><\/p>\n<p>&nbsp;<\/p>\n<p><strong>Past Paper Questions<\/strong><\/p>\n<p><a href=\"https:\/\/pastpapers.papacambridge.com\/viewer\/caie\/cambridge-upper-secondary-igcse-computer-science-0478-2015-jun-0478-s15-qp-12-pdf\">0478\/12 Paper 1 Theory May\/June 2015 &#8211; Qn 5<\/a><\/p>\n<p><a href=\"https:\/\/pastpapers.papacambridge.com\/viewer\/caie\/cambridge-upper-secondary-igcse-computer-science-0478-2016-jun-0478-s16-qp-11-pdf\">0478\/11 Paper 1 Theory May\/June 2016\u00a0\u00a0<\/a>Qn 9<\/p>\n<p><a href=\"https:\/\/pastpapers.papacambridge.com\/viewer\/caie\/cambridge-upper-secondary-igcse-computer-science-0478-2016-jun-0478-s16-qp-12-pdf\">0478\/12 &#8211; Paper 1 Theory May\/June 2016 Qn<\/a>4b<\/p>\n<p><a href=\"https:\/\/pastpapers.papacambridge.com\/viewer\/caie\/cambridge-upper-secondary-igcse-computer-science-0478-2016-nov-0478-w16-qp-11-pdf\">0478\/11 &#8211; Paper 1 Theory October\/November 2016 45d<\/a><\/p>\n<p><a href=\"https:\/\/pastpapers.papacambridge.com\/viewer\/caie\/cambridge-upper-secondary-igcse-computer-science-0478-2016-nov-0478-w16-qp-12-pdf\">0478\/12 &#8211; Paper 1 Theory October\/November 2016 Qn4<\/a><\/p>\n<p><a href=\"https:\/\/pastpapers.papacambridge.com\/viewer\/caie\/cambridge-upper-secondary-igcse-computer-science-0478-2017-jun-0478-s17-qp-11-pdf\">0478\/11 &#8211; Paper 1 Theory May\/June 2017 Qn 5<\/a><\/p>\n<p><a href=\"https:\/\/pastpapers.papacambridge.com\/viewer\/caie\/cambridge-upper-secondary-igcse-computer-science-0478-2018-oct-nov-0478-w18-qp-12-pdf\">0478\/12 &#8211; Paper 1 Theory October\/November 2018 qn 9b<\/a><\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Why do errors occur? When data is transferred through a network at each stage there is possibility that data might get corrupted. Therefore when a packet is received it needs to be checked to ensure the integrity of the data. Two common ways this can be achieved is through the use of\u00a0parity bits\u00a0and\u00a0check-sums. &nbsp; Parity&hellip;&nbsp;<a href=\"https:\/\/learnlearn.uk\/igcsecs\/error-detection\/\" class=\"\" rel=\"bookmark\">Read More &raquo;<span class=\"screen-reader-text\">Error Detection &#8211; Parity Bits, Check Digits &#038; Check Sums<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"on","neve_meta_content_width":81,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Error Detection &#8211; Parity Bits, Check Digits &#038; Check Sums | IGCSE Computer Science | Learnlearn.uk<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/learnlearn.uk\/igcsecs\/error-detection\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Error Detection &#8211; Parity Bits, Check Digits &#038; Check Sums | IGCSE Computer Science | Learnlearn.uk\" \/>\n<meta property=\"og:description\" content=\"Why do errors occur? 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Two common ways this can be achieved is through the use of\u00a0parity bits\u00a0and\u00a0check-sums. &nbsp; Parity&hellip;&nbsp;Read&hellip;","_links":{"self":[{"href":"https:\/\/learnlearn.uk\/igcsecs\/wp-json\/wp\/v2\/pages\/29"}],"collection":[{"href":"https:\/\/learnlearn.uk\/igcsecs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/learnlearn.uk\/igcsecs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/learnlearn.uk\/igcsecs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/learnlearn.uk\/igcsecs\/wp-json\/wp\/v2\/comments?post=29"}],"version-history":[{"count":16,"href":"https:\/\/learnlearn.uk\/igcsecs\/wp-json\/wp\/v2\/pages\/29\/revisions"}],"predecessor-version":[{"id":1040,"href":"https:\/\/learnlearn.uk\/igcsecs\/wp-json\/wp\/v2\/pages\/29\/revisions\/1040"}],"wp:attachment":[{"href":"https:\/\/learnlearn.uk\/igcsecs\/wp-json\/wp\/v2\/media?parent=29"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}