ISBN

An ISBN (International Standard Book Number) is a code identifying a particular edition and format of a book from a particular publisher. Newly assigned ISBNs have used the 13-digit ISBN-13 format since Jan. 1, 2007, replacing the original ISBN-10 format (International ISBN Agency). An ISBN-10 consists of nine decimal digits followed by a check digit that may be 0-9 or X, where X represents 10. All thirteen digits of an ISBN-13 are decimal.

An ISBN-10 has four elements, consisting of a registration group, publisher, publication, and check digit. An ISBN-13 has an additional initial three-digit prefix, either 978 or 979. The elements may be separated by hyphens or spaces. The registration group identifies a country, geographical region, or language area, not necessarily the language of the book. It contains one to five digits. Within the 978 prefix, examples include 0 and 1 for English-language areas, 2 for French-language areas, 3 for German-language areas, 4 for Japan, and 81 and 93 for India (International ISBN Agency).

The publisher element, also called the registrant element, identifies a publisher or imprint within its registration group. Its length varies, with shorter identifiers allowing larger blocks of publications. A publisher can have more than one block. The table gives examples of registration-group and publisher blocks used in ISBN-10 and, with the additional prefix 978, ISBN-13.

The publication element identifies a particular edition and format within the publisher's block. The registration group, publisher, and publication elements together contain nine digits. Thus, if the first two have lengths and , the publication element has length , allowing identifiers in that block. For a one-digit registration group, publisher elements of lengths two and seven allow one million and ten identifiers, respectively.

The final check digit is a checksum. Writing the successive values as , the ISBN-10 check digit is

(1)

where denotes the common residue of modulo . The value 10 is written as the Roman numeral X. In particular, a weighted sum divisible by 11 gives check digit 0, not 11.

For example, the ISBN-10 for the first edition of the printed version of MathWorld is 0-8493-9640-9, and

			(2)
			(3)
			(4)

where denotes a dot product and is the vector composed of the first 9 digits of the ISBN-10.

For ISBN-13, the corresponding rule uses alternating weights 1 and 3,

(5)

A weighted sum divisible by 10 gives check digit 0, not 10. An ISBN-10 is converted to ISBN-13 by prefixing 978 to its first nine digits and recalculating the check digit. For the example above,

			(6)
			(7)
			(8)

giving 978-0-8493-9640-3. ISBN-13 numbers beginning with 979 have no ISBN-10 equivalents.

Both checksums detect every single-digit substitution error, but neither makes the ISBN an error-correcting code when the erroneous position is unknown. The ISBN-10 checksum also detects every interchange of two unequal digits. For ISBN-13, interchanging two digits in positions with the same weight leaves the checksum unchanged. Interchanging unequal digits with different weights is undetected precisely when their values differ by 5. In particular, an interchange of adjacent unequal digits is detected except in this case.