Understanding Those Numbers

The International Standard Book Number, which appears on the back of most books as ISBN, is a unique number assigned to each book by its publisher, which assists in ordering, cataloging and identifying that particular book.

The ISBN system, which was adopted worldwide in 1972, is a very clever scheme for identifying books that includes a “check digit,” making it possible to tell whether there is an error in a number that has been received. This is an example of an error-correcting code, a mathematical scheme for detecting and correcting mistakes in the transmission of information.

Every ISBN contains 10 digits, of which the first nine identify the book, and the 10th is the check digit that enables someone to determine whether the first nine are correct.

For example, the ISBN of “The Honourable Schoolboy” by John Le Carre is 0-394-41645-7. The first number, or group code--in this case, 0, means that the book was published in the English-speaking world. The ISBN of all books published in the United States, the United Kingdom, Canada, Australia, New Zealand and South Africa begins with 0. The “group code” for Germany is 3; for Sweden it is 91.

The second group of numbers, 394, identifies the publisher, in this case, Alfred A. Knopf. In the United States, each publisher is assigned a publisher’s code by the ISBN Agency, which is part of the R. R. Bowker Co.

The third group of numbers, 41645 in this example, is assigned by the publisher to each of its books.

Which brings us to the last number, the check digit, which is calculated from the first nine in the following way:

Multiply the first digit by 10, the second digit by 9, the third digit by 8, the fourth digit by 7, and so forth, and then add the totals. In this example, the calculation produces (10 times 0) plus (9 times 3) plus (8 times 9) plus (7 times 4) plus (6 times 4) plus (5 times 1) plus (4 times 6) plus (3 times 4) plus (2 times 5), for a total of 27 plus 72 plus 28 plus 24 plus 5 plus 24 plus 12 plus 10 or 202.

Now, the check digit is the number that has to be added to 202 to make the total a multiple of 11. The next multiple of 11 is 209 (19 times 11), which means that the check digit is 7 (202 + 7 = 209). If 10 must be added to the total to make it a multiple of 11, the check digit is X.

When a publisher receives an order for a book, its computer can do this calculation in a jiffy and determine whether the check digit is what it should be.

The computer can then generate a short list of alternate ISBN’s that satisfy the “multiple-of-11 rule.” The publishing company can then figure out which book was intended. This scheme is preferable to shipping the wrong book.

Readers interested in more information about the ISBN system may write to the ISBN Agency, 205 E. 42nd St., New York, NY 10017.