TheInfoList

International Standard Book Number This check system – similar to the UPC check digit formula – does not catch all errors of adjacent digit transposition. Specifically, if the difference between two adjacent digits is 5, the check digit will not catch their transposition. For instance, the above example allows this situation with the 6 followed by a 1. The correct order contributes 3×6+1×1 = 19 to the sum; while, if the digits are transposed (1 followed by a 6), the contribution of those two digits will be 3×1+1×6 = 9. However, 19 and 9 are congruent modulo 10, and so produce the same, final result: both ISBNs will have a check digit of 7. The ISBN-10 formula uses the prime modulus 11 which avoids this blind spot, but requires more than the digits 0–9 to express the check digit.

Additionally, if the sum of th

This check system – similar to the UPC check digit formula – does not catch all errors of adjacent digit transposition. Specifically, if the difference between two adjacent digits is 5, the check digit will not catch their transposition. For instance, the above example allows this situation with the 6 followed by a 1. The correct order contributes 3×6+1×1 = 19 to the sum; while, if the digits are transposed (1 followed by a 6), the contribution of those two digits will be 3×1+1×6 = 9. However, 19 and 9 are congruent modulo 10, and so produce the same, final result: both ISBNs will have a check digit of 7. The ISBN-10 formula uses the prime modulus 11 which avoids this blind spot, but requires more than the digits 0–9 to express the check digit.

Additionally, if the sum of the 2nd, 4th, 6th, 8th, 10th, and 12th digits is tripled then added to the remaining digits (1st, 3rd, 5th, 7th, 9th, 11th, and 13th), the total will always be divisible by 10 (i.e., end in 0).

### ISBN-10 to ISBN-13 conversion

An ISBN-10 is converted to ISBN-13 by prepending "978" to the ISBN-10 and recalculating the final checksum digit using the ISBN-13 algorithm. The reverse process can also be performed, but not for numbers commencing with a prefix other than 978, which have no 10-digit equivalent.

### Errors in usage

Publishers and libraries have varied policies about the use of the ISBN check digit. Publishers sometimes fail to check the correspondence of a book title and its ISBN before publishing it; that failure causes book identification problems for libraries, booksellers, and readers. For example, ISBN 0-590-76484-5 is shared by two books – Ninja gaiden®: a novel based on the best-selling game by Tecmo (1990) and Wacky laws (1997), both published by Scholastic.

Most libraries and booksellers display the book record for an invalid ISBN issued by the publisher. The Library of Congress catalogue contains books published with invalid ISBNs, which it usually tags with the phrase "Cancelled ISBN". However, book-ordering systems such as