Calculation of Check Digits for Postal Orders, ISBN, and EAN, Summaries of Data Compression

Download Calculation of Check Digits for Postal Orders, ISBN, and EAN and more Summaries Data Compression in PDF only on Docsity! Page 1 of 6 Multimedia - Image Compression (1) Prepared by Dr. Omar A. Dawood 1 USPS money order number The US Postal office uses an identification number for postal orders. It’s an 11 digit number and the last number is the check digit as we have seen in other cases. Calculation of the check digit To calculate the check digit, add up the first 10 digits and the sum is divided by 9. The remainder is the check digit. Let's calculate the check digit for 84310325021. Check digit => 8+4+2+1+0+3+2+5+0+2+1 => 28 mod 9 => 1. Hence 1 is the check digit. International Standard Book Number (ISBN) This is a unique number created by Gordon Foster in 1961. The 10 digit format was developed by ISO (International Organization for Standardization). An ISBN is assigned to each edition of a book.  10 digit is assigned before Jan 1, 2007 and 13 digits is assigned after that.  Three parts: 1. the group identifier 2. the publisher code 3. the item number (title of the book).  Separated by spaces or hyphen.  Group Identifier: 1-5 digits (country, language).  The Publisher code: The national ISBN agency assigns the publisher number.  The publisher selects the item number. Example: 9971-5-0210-0, 0-943396-04-2, 0-85131-041-9 Calculation of the check digit  ISBN check digit (10 digits) - mod11 algorithm Page 2 of 6 Multimedia - Image Compression (1) Prepared by Dr. Omar A. Dawood 2 The last digit in an ISBN is the check digit, must range from 0 to 10. The ISBN uses a weighted system of checking. Each digit from left to right is assigned a weight from ten to one. Each digit is multiplied by its position weight and the resulting numbers are summed. Let's calculate the check digit for 0-07-063546-3.  ISBN check digit (13 digits) Each digit, starting from the left to right, is multiplied by 1 or 3 alternatively. The sum of the products modulo 10 gives us either zero or a number between 1 to 9. Subtract the number from 10 and it gives us the checksum. Hence 3 is the check digit. Here is an illustration: Page 5 of 6 Multimedia - Image Compression (1) Prepared by Dr. Omar A. Dawood 5 10 - 8 => 2 Hence 2 is the check digit. EAN The EAN-13 (European Article Number) is a 13 digit barcode which is a superset of the UPC (12 digits), and is used worldwide for marking products sold at retail points of sale (POS). EAN also indicates the country in which the company who sells the product is based in. Calculation of the check digit Verification: To verify the number, multiply the digits with 1 or 3 with respect to the position they have in the digits, starting from the left. Example: 8 901526 206056 1x8 + 3x9 + 1x0 + 3x1 + 1x5 + 3x2 + 1x6 + 3x2 + 1x0 + 3x6 + 1x0 + 3x5+ 1x6 => 8 + 27 + 3 + 5 + 6 + 6 + 6 + 18 + 15 + 6 => 100 mod10 => 0. Hence number is verified Calculation: We use the same method as above, however we will omit the last digit from the calculation because that is the digit we want to find. Here if the remainder is a non-zero number then it is subtracted from 10. Example: 8 901526 206056 1x8 + 3x9 + 1x0 + 3x1 + 1x5 + 3x2 + 1x6 + 3x2 + 1x0 + 3x6 + 1x0 + 3x5 => 8 + 27 + 3 + 5 + 6 + 6 + 6 + 18 + 15 => 94 mod10 => 6. 10 - 4 = > 6. Hence 6 is the check digit. Page 6 of 6 Multimedia - Image Compression (1) Prepared by Dr. Omar A. Dawood 6 REF: [1] "Data Compression: The Complete Reference", by David Salomon, Fourth Edition, 2007, Springer. [2] "Fundamentals of Multimedia", by: Li and Drew, 2004, Prentic Hall. https://www.ece.ucdavis.edu/cerl/reliablejpeg/compression/