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Each of the first nine digits of the 10-digit ISBN—excluding the check digit itself—is multiplied by its (integer) weight, descending from 10 to 2, and the sum of these nine products found. The value of the check digit is simply the one number between 0 and 10 which, when added to this sum, means the total is a multiple of 11.
10. This system thus detects all single-digit substitution and transposition errors (including jump transpositions), but at the cost of the check digit possibly being 10, represented by "X". (An alternative is simply to avoid using the serial numbers which result in an "X" check digit.) ISBN-13 instead uses the GS1 algorithm used in EAN numbers.
ISBN-10 and ISBN-13 use different check digit algorithms to compute the last digit of the ISBN. The following tools will convert any ISBN-10 to an ISBN-13 along with the correct check digit value. Nihiltres' ISBN tool; ISBN converter of the U.S. Library of Congress; ISBN converter of ISBN.org; Stylistically, please:
The checksum digit is the digit which must be added to this checksum to get a number divisible by 10 (i.e. the additive inverse of the checksum, modulo 10). [8] See ISBN-13 check digit calculation for a more extensive description and algorithm. The Global Location Number (GLN) also uses the same method.
The GS1 Identification Key is used to identify physical locations or legal entities. The key comprises a GS1 Company Prefix, Location Reference, and Check Digit. Location identified with GLN could be a physical location such as a warehouse or a legal entity such as a company or customer or a function that takes place within a legal entity.
Check digit. To detect transcription errors in which digits have been altered or transposed, the last digit of a pre-2007 ISBN must match the result of a mathematical formula incorporating the other 9 digits (ISBN-10 check digits).
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; 99900–99999; The following must have a 979- prefix:
The Global Trade Item Number (GTIN) is an identifier for trade items, developed by the international organization GS1. [1] Such identifiers are used to look up product information in a database (often by entering the number through a barcode scanner pointed at an actual product) which may belong to a retailer, manufacturer, collector, researcher, or other entity.