# 5. Check Digit

This is used when you want to be sure that a range of numbers has been entered correctly. There are many different schemes (algorithms) for creating check digits.

For example, the ISBN-10 numbering system for books makes use of 'Modulo-11' division. In modulo division, the answer is the remainder of the division. For example

8 Mod 3 = 2 i.e. the remainder of dividing 8 by 3 is 2.

Consider the ISBN number:

ISBN 1 84146 201 2

The check digit is the final number in the sequence, so in this example it is the final ‘2’.

The computer will perform a complex calculation on all of the numbers and then compare the answer to the check digit.  If both match, it means the data was entered correctly.

### Using the check digit to calculate whether a code is correct

##### Step 1

Remove the last digit from the ISBN number

ISBN 1 84146 201 2

In the above example, the last digit would be the 2.

##### Step 2a

Write out the remaining numbers starting from the right hand number in the ISBN.

 ISBN 1 8 4 1 4 6 2 0 1
##### Step 2b

Put a 10 underneath the first number, 9 under the second etc

 ISBN 1 8 4 1 4 6 2 0 1 Code 10 9 8 7 6 5 4 3 2
##### Step 2c

Multiply the number by the code underneath it

 ISBN 1 8 4 1 4 6 2 0 1 Code 10 9 8 7 6 5 4 3 2 Result 10 72 32 7 24 30 8 0 2
##### Step 3

Add the results from the bottom row together:

10 + 72 + 32 + 7 + 24 + 30 + 8 + 0 + 2 = 185

##### Step 4

Divide the total by 11 and record the remainder

185 divide by 11 = 16 with 9 remaining.

##### Step 5

Take the remainder away from 11.

11 - 9 (the remainder from step 4) = 2

##### Step 6

Compare the answer from step 5 with the original check digit that you removed in step 1.

Step 1 check digit removed = 2

If the numbers are the same then the check digit has confirmed the original numbers were entered correctly.

NOTE:

If the remainder is 0 then the check digit is 0

If the remainder is 10 then the check digit is X

For example, work out the check digit for ISBN 184146208, which should be X

And for a zero check digit, work out ISBN 184146202.

challenge see if you can find out one extra fact on this topic that we haven't already told you

Click on this link: ISBN check digit