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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.

Contents

Examples

UPC

ISBN 10

Other examples of check digits

External links

Examples

UPC

The final digit of a Universal Product Code is a check digit computed as follows:
# Add the digits in the odd-numbered positions (first, third, fifth, etc.) together and multiply by three.
# Add the digits in the even-numbered positions (second, fourth, sixth, etc.) to the result.
# Subtract the result from the next-higher multiple of ten. The answer is the check digit.
For instance, a UPC-A barcode (In this case, a UPC for a box of tissues) "03600029145X" where ''X'' is the check digit, ''X'' can be calculated by adding the odd-numbered digits (0+6+0+2+1+5 = 14), multiplying by three (14 × 3 = 42), adding the even-numbered digits (42+3+0+0+9+4 = 58) and subtracting from the next-highest multiple of ten (60 - 58 = 2). The check digit is thus 2.

ISBN 10

The final character of a ten digit International Standard Book Number is a check digit computed so that multiplying each digit by its position in the number (counting from the right) and taking the sum of these products modulo 11 is 0. The last digit (which is multiplied by 1) is the check digit, chosen to make the sum correct. It may need to have the value 10, which is represented as the letter X. For example, take the ISBN 0-201-53082-1. The sum of products is 0×10 + 2×9 + 0×8 + 1×7 + 5×6 + 3×5 + 0×4 + 8×3 + 2×2 = 98 modulo 11 (10) subtracted from 11 ≡ 1. So the ISBN is valid.
While this may seem more complicated than the first scheme, it 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.
ISBN 13 (in use January, 2007) generates its check digit the same way as the UPC, except the even digits are multiplied by 3 instead of the odd digits.

Other examples of check digits

★ The tenth digit of the National Provider Identifier for the healthcare industry more

★ The Australian Tax File Number (based on modulo 11)

★ The ninth digit of a Canadian Social Insurance Number (SIN)

★ The North American CUSIP number

★ The International SEDOL number

★ The International Securities Identifying Number (ISIN)

★ The International CAS registry number's final digit.

★ Modulo 10 check digits in credit card account numbers, calculated with the Luhn algorithm.

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★ Also used in the Norwegian KID (customer identification number) numbers used in bank giros (credit transfer).

★ The final character encoded in a magnetic stripe card is a computed Longitudinal redundancy check

★ final digit of a POSTNET code

★ final digit of an ISSN code

★ final digit of a DUNS number (though this is scheduled to change, such as that the final digit will be chosen freely in new allocations, rather than being a check digit)

★ The Spanish fiscal identification number (número de identificación fiscal, NIF), (based on modulo 23).

★ The ninth digit of a Vehicle Identification Number (VIN).

★ The ninth digit of an Israeli Teudat Zehut (Identity Card) number.

★ The 13th digit of Former Yugoslav Unique Master Citizen Number (JMBG)

★ Last check digit in EAN/UPC serialisation of Global Trade Identification Number (GTINs). It applies to GTIN-8, GTIN-12, GTIN-13 and GTIN-14.

★ The seventh character of a New Zealand NHI Number.
Compare to check bit.

External links

★ Identification numbers and check digit schemes (a mathematical explanation of various check digit schemes)