Category:International Standard Book Numbers

This category contains results about International Standard Book Numbers.
Definitions specific to this category can be found in Definitions/International Standard Book Numbers.

An International Standard Book Number is a codeword made up of digits used to uniquely identify a published book.

One of the digits represents the language in which the book is written.

Two of the digits represent the publisher.

There is also a check digit to detect transcription errors.

ISBN-$10$

The ISBN-$10$ format consists of a string of $9$ digits followed by a check digit in the set $\set {0, 1, \ldots, 9, X}$.

The check digit $d$ is calculated as follows.

Let $c$ be calculated as:

$c = \ds \sum_{k \mathop = 1}^9 k d_k \pmod {11}$

where $d_k$ denotes the $k$th digit in the ISBN-$10$.

Then the check digit $d$ is defined as:

$d = \begin {cases} c & : c \le 9 \\ X &: c = 10 \end {cases}$

ISBN-$13$

The ISBN-$13$ format consists of a string of $12$ digits followed by a check digit.

The check digit $d$ is calculated as:

$d = \ds \sum_{k \mathop = 1}^{12} k d_k \pmod {10}$