The 10-digit International Standard Book Number (ISBN) format was developed by the International Organization for Standardization and published as an international standard, ISO 2108, in 1970. (However, the 9-digit SBN code was used in the UK until 1974.) Currently, the ISO TC 46/SC 9 is responsible for the standard.
Since 1 January 2007, International Standard Book Numbers have been of 13 digits, compatible with Bookland EAN-13s.
The group identifier is a 1 to 5 digit number. The single digit group identifiers are: 0 or 1 for English-speaking countries; 2 for French-speaking countries; 3 for German-speaking countries; 4 for Japanese; 5 for Russian, and 7 for Chinese. An example 5 digit group identifier is 99936, for Bhutan.
By using variable block lengths, a large publisher will have few digits allocated for the publisher number and many digits allocated for titles; likewise countries publishing much will have few allocated digits for the group identifier, and many for the publishers and titles.
A listing of all the 628,000 assigned publisher codes is published, and can be ordered in book form (€558, US$915.46).
Publishers receive blocks of ISBNs, with larger blocks allotted to publishers expecting to need them; a small publisher may receive ISBNs of one or more digits for the group identifier code, several digits for the publisher, and a single digit for the individual items. Once that block of ISBNs is used, the publisher may receive another block of ISBNs, with a different publisher number. Consequently, a publisher may have different allotted publisher numbers. There also may be more than one group identifier used in a country. This might occur if a popular identifier has used up all of its numbers.
The 2001 edition of the official manual of the International ISBN Agency says that the ISBN-10 check digit — which is the last digit of the ten-digit ISBN — must range from 0 to 10 (the symbol X is used instead of 10) and must be such that the sum of all the ten digits, each multiplied by the integer weight, descending from 10 to 1, is a multiple of the number 11. Modular arithmetic is convenient for calculating the check digit using modulus 11. Each of the first nine digits of the ten-digit ISBN — excluding the check digit, itself — is multiplied by a number in a sequence from 10 to 2, and the remainder of the sum, with respect to 11, is computed. The resulting remainder, plus the check digit, must equal 11; therefore, the check digit is 11 minus the remainder of the sum of the products.
For example, the check digit for an ISBN-10 of 0-306-40615-? is calculated as follows:
s = 0×10 + 3×9 + 0×8 + 6×7 + 4×6 + 0×5 + 6×4 + 1×3 + 5×2
= 0 + 27 + 0 + 42 + 24 + 0 + 24 + 3 + 10
= 130
130 / 11 = 11 remainder 9
11 - 9 = 2
Formally, the check digit calculation is:
click here
The calculation of an ISBN-13 check digit begins with the first 12 digits of the thirteen-digit ISBN (thus excluding the check digit itself). Each digit, from left to right, is alternately multiplied by 1 or 3, then those products are summed modulo 10 to give a value ranging from 0 to 9. Subtracted from 10, that leaves a result from 1 to 10. A zero (0) replaces a ten (10), so, in all cases, a single check digit results.
This check system — similar to the UPC check digit formula — does not catch all errors of adjacent digit transposition. Specifically, if the difference between two adjacent digits is 5, the check digit will not catch their transposition.
from http://en.wikipedia.org/wiki/ISBN
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2.) What the hell's a check digit?
A check digit is a form of redundancy check used for error detection, the decimal equivalent of a binary checksum. It consists of a single digit computed from the other digits in the message.
With a check digit, one can detect simple errors in the input of a series of digits, such as a single mistyped digit, or the permutation of two successive digits.
[the ISBN check digit] can be validated very simply by adding all the products together then dividing by 11. If the result is an integer then the ISBN is valid.
Other examples of check digits:
The ninth digit of a Canadian Social Insurance Number (SIN)
Modulo 10 check digits in credit card account numbers, calculated with the Luhn algorithm.
The final character encoded in a magnetic stripe card is a computed Longitudinal redundancy check
UPC
I still don't think I fully understand.
from http://en.wikipedia.org/wiki/Check_digit
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