Another barcode system is the International Standard Book Number, or ISBN. This system was developed in the late 1960s and early 1970s so that every book could have a special 10-digit identification number.

This ten-digit number is composed of blocks of numbers identifying the language or country, the publisher, and the item number or edition for that publisher. The tenth digit is the check digit.

Beginning January 1, 2007, the ISBN system was replaced by the ISBN-13 system. It is a 13-digit number beginning with 978, followed by the current nine digits of the ISBN, and it will have a new check digit. When all old ISBNs have been used, the next series will begin with 979.

The check digit is determined using a method similar to the one used to determine the check digit for a UPC number.

For the older 10-digit numbers, the check digit is calculated by multiplying the first digit by 10, the second by 9, the third by 8, and continuing until the ninth digit is multiplied by 2. The sum of those products and the check digit must be a multiple of 11. That is, the check digit is the number that is added to the sum of products to reach the next highest multiple of 11.

One problem that arises in this process is that the check digit might need to be a 10. Because we only have digits 0-9, an X is written in the check-digit place in this case. (X is the Roman numeral for 10.)