### ISBN Number (10/19/2001)

Prepared by:

Joseph Malkevitch

Mathematics and Computing Department

York College (CUNY)

Jamaica, NY 11451

Email: malkevitch@york.cuny.edu (for additions, suggestions, and corrections)

ISBN stands for International Standard Book Number. It was developed to have a system
for identifying and tracking books for libraries, publishers, and consumers. The
number consists of 10 "digits" separated by into 4 variable length fields by dashes.
A typical ISBN number would be: 0-7167-2841-9. The first field is the language of the
target area for the book. 0 is used for books targeted at an English speaking audience.
The next block of digits is a publisher identification number. The third block is
the item number in the particular publisher's line of books. The last field, is a single
symbol, which is a 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or X. This field provides a check
symbol which enables one to detect errors. Errors which occurs because a single digit
of an actual ISBN number is wrong or which occurs because two digits are interchanged,
whether they are in adjacent positions or not will be detected. The check symbol
is chosen based on the earlier digits as follows. If reading from left to right,
the symbols in the ISBN number are: a1, a2, ..., a10 where a10 denotes the check symbol, then a10 is chosen so that 10(a1) + 9(a2) + ... + 2(a9) + a10 is divisible by 11 with a zero remainder. Since the remainders after division by
11 can be any number from 0 to 10, the check symbol might have two digits if the
remainder is 10. To avoid this problem instead of using the two digits 10 in this
case, the Roman symbol for 10, namely X, is used instead. Some publishers in order to avoid the
use of the X as a check symbol, modify the item numbers that they use to avoid the
appearance of X.

References:

Malkevitch, J. et al, For All Practical Purposes, Fifth Edition, W. H. Freeman, New York, 2000.

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