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### Check Digits in Payroll or Stock Numbers

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Date: 11/16/96 at 18:28:36
From: Nigel Tombs
Subject: Check Digits

Hi Dr. Math:

Have you ever used or do you know about check digits?  They appear in
payroll numbers or stock numbers.

I understand it's a unique single digit number that is placed as the
last number of a series of numbers and is made from a calculation
involving all of the other numbers.  A computer checks the last digit
to verify that it is a correctly entered stock number from a user
input.  If the user enters an incorrect number, the transaction will
be rejected.

For example: stock number 4793769(?), where (?) is the calculated
digit.

What is the set of calculations required to get the unique single
digit number?  Does the computer generate it automatically?  I assume
the user does not see the last digit since only the computer program
is concerned with it.

Nigel, Swindon, England
```

```
Date: 11/16/96 at 19:10:03
From: Doctor Mike
Subject: Re: Check Digits

Hello Nigel,

Yes, I am familiar with check digits that are used for many things.

One example that I ran across recently has to do with SIN numbers,
which are Social Insurance Numbers for citizens of Canada.  Look at
the web site:

http://www.revcan.ca/E/pub/gd/402895et/402895e.txt

and search for the text string "check digit".  This gives the
calculation actually used by the government for calculating the 9th
digit from the first 8 digits.  It is pretty involved, and I don't
know why they didn't choose something a little simpler, but that is
what they use.

There are many different calculations for producing a check digit, and
not just one standard one.  In fact, some calculations may be kept
secret for security reasons.  A very simple one that could be used
for checking for data entry errors would be to add up the other
digits, and take the units digit of that result as the check digit.
Using this process with your example 4793769(?) would give 47937695
since the other digits add up to 45.  This is NOT a very good check
digit algorithm because it fails to catch a very common mistake of
entered 47973695, you would not catch this with the simple check digit
algorithm.  The reason is that the other digits added up in ANY order
still give 45, so 5 would still be the check digit. This is one reason
for a more involved check digit calculation like the one in the

I hope this helps.

-Doctor Mike,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Calculators, Computers

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