Product

9

21

8

0

1

3

0

0

6

2

6

56

0

**Step 2**

: Divide the sum of the weighted products of the first 12 digits of the ISBN

calculated in step 1 by 10, determining the remainder.

56 / 10 = 5 remainder = 6

**Step 3**

: Subtract the remainder calculated in step 2 from 10. The resulting difference is the

value of the check digit with one exception. If the remainder from step 2 is 0, the check

digit is 0.

10 6 = 4

Check digit = 4

ISBN = 978 0 11 000222 4

The following mathematical formula is an alternative way of expressing the calculation of

the check digit:

Check digit = mod 10 (10 [mod 10 {sum of weighted products of the first 12 ISBN digits}])

Check digit = mod 10 (10 [mod 10 {56}])

Check digit = 4

The sum of the weighted products of the first 12 digits plus the check digit must be

divisible by 10 without a remainder for the ISBN to be valid.

*Note:*

The length of the registration group, registrant, and publication elements are variable

and may not always be the same as in the example table above. Not all registration group

and registrant combinations are valid. See

*Distribution of ranges*

section for formulaic

information required to validate and split an ISBN.

Please contact your local registration agency, which will be able to assist you with

calculating your ISBNs either by providing pre calculated lists of the ISBNs or by providing

software to enable you to calculate your own ISBNs.

**4.6 Distribution of ranges **

Ranges are allocated according to anticipated demand (i.e., the size of the publishing

programme) within a particular regional or language grouping. Some registration group

elements are held in reserve by the International ISBN Agency to ensure future capacity.

The International ISBN Agency will allocate these as necessary when ranges are low in

any particular grouping. Additionally, registrant ranges within a registration group that has

already been allocated to a specific regional or language grouping may remain undefined

to satisfy future needs.

Comprehensive details of registration groups and registrant range metadata is available

from the International ISBN Agency and enables the validation of the current allocation of

defined ranges. Not all registration group and registrant combinations are valid. The

formulaic information (using the comprehensive group and registrant range metadata)

11

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