The Math Hidden Within ISBN Numbers

An ISBN (or International Standard book Number) is a 13-digit number uniquely identifying books and “book-like” products. The number is used to differentiate one title, or edition of a title, from a specific publisher.  For example, an e-book and a paperback version of the same book would each have different ISBNs. Changing the cover of a book does not result in a new edition, since the text is the same.

Not all books have an ISBN number. If the book is printed privately and is not intended for bookstore or library distribution, then it does not need an ISBN number.

ISBN numbers were first derived in 1967 in the United Kingdom by David Whitaker, who based the system upon the 9-digit Standard Book Number (SBN) created in 1966. The 10-digit format was then developed the International Organization for Standardization  (ISO) and published in 1970. Ironically, the UK continued to use the 9-digit SBN code until 1974. Old SBNs were converted to ISBNs by adding a zero prefix. ISBNs remained 10-digits long until January 1, 2007, when ISBNs switched to a 13-digit format.

The number is divided into five parts of variable length, each separated by a hyphen:

1. A Prefix (only applicable to 13-digit ISBNs). To date, only “978” or “979” have been used.
2. Identifier for national or geographic location of the publisher
3. The publisher identifier
4. The title identifier which differentiates a particular title or edition
5. A check digit which validates the ISBN.

For my fellow math geeks out there, the check digit for an ISBN-13 number is calculated via the following procedure:

• Multiply each of the preceding 12-digits by a 1 or a 3 (alternating, starting with 1)
• Sum all the products
• Divide the result by 10 and calculate the remainder (mod 10)
• Subtract the remainder from 10

For the ISBN-13 number for Apricots and Wolfsbane: 978-1-946802-02-6, the check digit (6), is calculated:

Fun fact: The check digit for ISBN-10 numbers is calculated differently.  The procedure can result in a “10” for a check digit. When this occurs, the last digit is replaced with a roman numeral X to maintain a 10-digit ISBN Number.

For more information visit:

http://www.isbn.org/faqs_general_questions
https://en.wikipedia.org/wiki/International_Standard_Book_Number