Check Digits in Payroll or Stock Numbers

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.

Thanks in advance for any answers or theory you may provide.

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 
switching adjacent digits.  If instead of entering 47937695 you 
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 
Canadian system. 
  
I hope this helps.

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/