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# 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.

## Examples

### UPC

The final digit of a Universal Product Code is a check digit computed as follows:

1. Add the digits (up to but not including the check digit) in the odd-numbered positions (first, third, fifth, etc.) together and multiply by three.
2. Add the digits (up to but not including the check digit) in the even-numbered positions (second, fourth, sixth, etc.) to the result.
3. If the last digit of the result is 0, then the check digit is 0.
4. If the last digit of the result is not zero, then subtract the last digit from 10. The answer must equal the check digit.

For instance, the UPC-A barcode for a box of tissues is "036000291452". The last digit is the check digit "2", and if the other numbers are correct then the check digit calculation must produce 2.

1. We add the odd number digits 0+6+0+2+1+5 = 14, and multiply by 3 to get 14 × 3 = 42.
2. We add the even number digits to this result 42+3+0+0+9+4 = 58.
3. The last digit is 8, we subtract this from 10 to get 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

ISBN 13 (in use January, 2007) is equal to the EAN-13 code found underneath a book's barcode. Its check digit is generated the same way as the UPC, except the even digits are multiplied by 3 instead of the odd digits.

### EAN (GLN,GTIN, EAN numbers administered by GS1)

EAN (European Article Number) check digits (administered by GS1) - are calculated by summing the even position numbers and multiplying by 3, then adding the sum of the odd position numbers. The final digit of the result is subtracted from 10 to calculate the check digit (or left as is if already zero). A GS1 check digit calculator and detailed documentation is online at GS1's website.

### Other examples of check digits

Compare to check bit.

• Modulo 97 check digits in a Belgian bank account number