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Appendix 1 of the International ISBN Agency's official user manual [16]: 33 describes how the 13-digit ISBN check digit is calculated. The ISBN-13 check digit, which is the last digit of the ISBN, must range from 0 to 9 and must be such that the sum of all the thirteen digits, each multiplied by its (integer) weight, alternating between 1 and 3 ...
For instance, the UPC-A barcode for a box of tissues is "036000241457". The last digit is the check digit "7", and if the other numbers are correct then the check digit calculation must produce 7. Add the odd number digits: 0+6+0+2+1+5 = 14. Multiply the result by 3: 14 × 3 = 42. Add the even number digits: 3+0+0+4+4 = 11.
A UPC barcode. The Universal Product Code (UPC or UPC code) is a barcode symbology that is used worldwide for tracking trade items in stores.. The chosen symbology has bars (or spaces) of exactly 1, 2, 3, or 4 units wide each; each decimal digit to be encoded consists of two bars and two spaces chosen to have a total width of 7 units, in both an "even" and an "odd" parity form, which enables ...
The check digit is computed as follows: If the number already contains the check digit, drop that digit to form the "payload". The check digit is most often the last digit. With the payload, start from the rightmost digit. Moving left, double the value of every second digit (including the rightmost digit). Sum the values of the resulting digits.
Verhoeff had the goal of finding a decimal code—one where the check digit is a single decimal digit—which detected all single-digit errors and all transpositions of adjacent digits. At the time, supposed proofs of the nonexistence [6] of these codes made base-11 codes popular, for example in the ISBN check digit.
In 2007, the length of an ISBN changed from 10 to 13 digits, and a new 3-digit prefix (978 or 979) was added in front of 10-digit ISBNs. [ 2] The following registration groups are compatible with or without a 978- prefix: 0–5. 600–639. 64–69. 7. 80–94. 950–989. 9900–9989.
The EAN-8 code is an eight-digit barcode used usually for very small articles, such as chewing gum, where fitting a larger code onto the item would be difficult. Note: the equivalent UPC small format barcode, UPC-E, encodes a GTIN-12 with a special Company Prefix that allows for "zero suppression" of four zeros in the GTIN-12. The GS1 encoding ...
The Damm algorithm generates only 10 possible values, avoiding the need for a non-digit character (such as the X in the 10-digit ISBN check digit scheme). Prepending leading zeros does not affect the check digit (a weakness for variable-length codes). [1]