Check digit - Definition and Overview

In computers and telecommunication, a check digit is a simple form of redundancy check used for error detection. It consists of a single digit computed from the other digits in the message.

The final digit of a Universal Product Code is a check digit computed so that summing the even-numbered digits with 3 times the odd-numbered digits, modulo 10, is 0. For example, take the UPC 070617006092. The sum of even numbered digits is 7+6+7+0+0+2 = 22 and 3 times the sum of the odd-numbered digits is 3 × (0+0+1+0+6+9) = 48; the total sum is 22+48 = 70 = 0 modulo 10. So the code is valid.

The final character of an International Standard Book Number is a check digit computed by multiplying each digit by its position in the number and taking the sum of these products modulo 11 (if the result is 10, the check digit is the letter X). For example, take the ISBN 0201530821. The sum of products is 0×1 + 2×2 + 0×3 + 1×4 + 5×5 + 3×6 + 0×7 + 8×8 + 2×9 = 133 = 1 modulo 11. So the check digit is 1 and the ISBN is valid.

Other examples of Check digits

• The Australian Tax File Number (based on modulo 11)
• The North American CUSIP number
• Modulo 10 check digits in Credit card account numbers, calculated with the Luhn algorithm.

Compare to check bit.