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A check digit is a form of redundancy check used for error detection on identification numbers, such as bank account numbers, used in an application where they will sometimes be input manually. It consists of one or more digits computed by an algorithm from the other digits (or letters) in the sequence input.
With a check digit, one can detect simple errors in the input of a series of characters (usually digits), such as a single mistyped digit or some permutations of two successive digits1.
The International Standard Book Number (ISBN) is a unique numeric commercial book identifier. Publishers purchase ISBNs from an affiliate of the International ISBN Agency. The 10-digit ISBN format was developed by the International Organization for Standardization (ISO) and was published in 1970 as an international standard ISO 2108.
The 2001 edition of the official manual of the International ISBN Agency says that the ISBN-10 check digit – where the last digit of the ten-digit ISBN – must range from 0 to 10 (the symbol X is used for 10) and must be such that the sum of all the ten digits, each multiplied by its (integer) weight, descending from 10 to 1, is a multiple of 11.2
Below you can find the calculator which generates check digit from 9-digits sequence, forming final 10-digits sequence, and validates 10-digits sequence using mod 11 algorithms described by ISBN.