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.

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   3 6   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.

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