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 5 answer = 2

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