ISBN Check Digit Calculation

Introdutction:

The check digit is the last digit of an ISBN.
It is calculated on a modulus 11 with weights 10-2,
using X in lieu of 10 where ten would occur as a check digit.

This means that each of the first nine digits of the ISBN
 – excluding the check digit itself –
is multiplied by a number ranging from 10 to 2 and
that the resulting sum of the products,
plus the check digit,
must be divisible by 11 without a remainder.

Example:

ISBN 0-8436-1072-7:

	Group identifier		Publisher prefix					Title identifier					Check digit
ISBN	0			8	4	3	6		1	0	7	2	7
Weight	10			9	8	7	6		5	4	3	2
Products	0			+72	+32	+21	+36		+5	+0	+21	+4	+7

Total: 198

As 198 can be divided by 11 without remainder 0-8436-1072-7 is a valid ISBN.
7 is the valid check digit.