Check digit in ISBN-13

Introduction:

From Jan 1, 2007 all ISBN will transfer from 10 digit to 13 digital.
The check digit algorithm of the check digit is also changed.

Algorithm:

The calculation of an ISBN-13 check digit begins with the first 12 digits
of the 13-digit ISBN (thus excluding the check digit itself).
Each digit from left to right is multiplied alternately by 1 or 3,
then these products are summed modulo 10 to give a value from 0 to 9.
Subtracted from 10, this leaves a result from 1 to 10. A 10 is replaced by a 0,
so in all cases a single check digit emerges.

Example:

the ISBN-13 check digit of 978-0-306-40615-? is calculated as follows

s = 9×1 + 7×3 + 8×1 + 0×3 + 3×1 + 0×3 + 6×1 + 4×3 + 0×1 + 6×3 + 1×1 + 5×3
   =   9 +  21 +   8 +   0 +   3 +   0 +   6 +  12 +   0 +  18 +   1 +  15
  = 93
 93 / 10 = 9 remainder 3
10 – 3 = 7

Thus the check digit is 7, and the complete sequence is ISBN 978-0-306-40615-7.