One of the examples of a weighted checksum is the ISBN-10 code we see printed on the back cover of some books. In ISBN-10, there are 9 decimal digits that define the country, the publisher, and the book. The tenth (rightmost) digit is a checksum digit. The code, D₁D₂D₃D₄D₅D₆D₇D₈D₉C, satisfies the following.

In other words, the weights are 10, 9, . . .,1. If the calculated value for C is 10, one uses the letter X instead. By replacing each weight w with its complement in modulo 11 arithmetic (11 ˆ’ w), it can be shown that the check digit can be calculated as shown below.

Calculate the check digit for ISBN-10: 0-07-296775-C.

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[(10 × D1) + (9 × D2) + (8 × D3) + ...+ (2 × D9) + (1 × C)] mod 11 = 0 C = [(1 × D1) + (2 × D2) + (3 × D3) + . . .+ (9 × D9)] mod 11