An International Standard Book Number (ISBN) is a code used to uniquely identify a book together. It also uniquely encodes the book's publisher and includes information about its language of authorship. The original 10-"digit" ISBN-10 (where a "digit" consists of a decimal digit 0-9 for the first 9 places and 0-9 or X for the tenth place, corresponding to a mixed base string), in use for more than 30 years, was officially replaced with a 13-digit ISBN-13 (where each place is truly a decimal digit) as of Jan. 1, 2007.

The digits of an ISBN d_i are arranged in four groups (for an ISBN-10) or five groups (for an ISBN-13), which are sometimes (but not always) separated by hyphens. At present, an ISBN-13 is always prefixed by the digits 978 (US ISBN Agency). The first group in ISBN-10 or the second group for an ISBN-13 is a single digit which encodes country or language in which a publisher is incorporated: 0 for English, 2 for French, 3 for German, 4 for Japanese, 8 for Indian publishers, etc. The next group of digits specifies the publisher, and may range in length from two to seven digits, with fewer digits used for larger publishers. Some publishers with offices in more than one country (at least when different languages are spoken in those countries) have multiple publisher codes and initial digits.

publisherpublisher block
American Mathematical Society0-821
Birkhäuser Basel3-7643
Birkhäuser Boston0-8176
Cambridge University Press0-521
CRC Press0-8493
Oxford University Press0-198
Springer Berlin3-540
Springer New York0-387
Tarquin Publications0-906212

The next group of digits specifies an individual book, and may be from one to six digits in length. The actual number is eight minus the number of digits in the publisher group, so that small publishers may have only 10 books while large ones can have up to a millions books. The last digit is a check digit which may be in the range 0-9 or X (where X is the Roman numeral for 10) for an ISBN-10, or 0-9 for an ISBN-13.

For ISBN-10, the check digit is computed from the equation

 d_(10)=11-[10d_1+9d_2+8d_3+...+2d_9 (mod 11)].

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

ISBN10=11-[(10,9,8,7,6,5,4,3,2)·(0,8,4,9,3,9,6,4,0) (mod 11)]
=11-[266 (mod 11)]

where a·b denotes a dot product and (0,8,4,...) is the vector composed of the first 9 digits of the ISBN-10.

The scheme used by 978- and (future) 979-prefixed ISBN-13, is instead given by

 d_(13)=10-[d_1+3d_2+d_3+3d_4+...+d_(11)+3d_(12) (mod 10)]

(Book Industry Study Group). Therefore, the ISBN-13 corresponding to the ISBN-10 above would have check digit

ISBN13=10-[(1,3,1,3,1,3,1,3,1,3,1,3)·(9,7,8,0,8,4,9,3,9,6,4,0) (mod 10)]
=10-[107 (mod 10)]

and so would be 978-0-8493-9640-3.

The ISBN is error-detecting, but not error-correcting (unless it is known that only a single digit is erroneous). The ISBN detects any single-digit error, as well as most two-digit error resulting from transposing two digits.

See also

Code, Coding Theory, UPC

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Book Industry Study Group. "Are You Ready for ISBN-13: Conversions and Calculations.", S. and Flannery, D. In Code: A Mathematical Journey. London: Profile Books, pp. 116-118, 2000.Hill, R. First Course in Coding Theory. Oxford, England: Oxford University Press, 1986.Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, p. 894, 1992.U.S. ISBN Agency. "ISBN Assignments, SAN, Bookland EAN Bar Code Symbols, Technical Information and Advice."

Referenced on Wolfram|Alpha


Cite this as:

Weisstein, Eric W. "ISBN." From MathWorld--A Wolfram Web Resource.

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