Check digit

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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.

1 Examples
2 External links

[edit] Examples

[edit] 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-higher multiple of ten (60 - 58 = 2). The check digit is thus 2.

[edit] 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 + 1×1 = 99 modulo 11 ≡ 0. So the ISBN is valid.

While this may seem more complicated than the first scheme, it can actually compute very simply using two sums, both initialized to 0:

sum1 = sum2 = 0
for (each digit of the ISBN)
    sum1 = sum1 + digit
    sum2 = sum2 + sum1

the final sum2 should be a multiple of 11.

ISBN 13 (in use January, 2007) generates its check digit the same way as the UPC.

[edit] Other examples of check digits

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 CAS registry number's final digit.
Modulo 10 check digits in credit card account numbers, calculated with the Luhn algorithm.
- Also used in the Norwegian KID (customer identification number) numbers used in bank giros (credit transfer).
final digit of a POSTNET code
final digit of an ISSN code
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)