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Bar Codes and Check Digits

Date: 10/13/2001 at 23:02:57
From: Melissa DeSouza
Subject: Bar Codes

Dr. Math,

I've been looking through books, the Internet, articles, and other 
resources about Bar Codes. I understand their application to the real 
world, but don't understand how it could be used in a science/math 
fair. I don't understand what they have to do with math. I find bar 
codes under sections of math. Can you please tell me why?
I would greatly appreciate it. 

Thank you!

Date: 10/14/2001 at 02:27:22
From: Doctor Jeremiah
Subject: Re: Bar Codes

Hi Melissa,

Bar codes have a lot to do with math. A string of numbers has to be 
represented by bars. How many bars does it take to represent one 
number and what different widths of bars?

Also, because bar code readers might make a mistake, error-checking 
bars are used to check the answer. This is the same as any other 
string of numbers. The last number on a credit card number is a check 
digit used to decide whether the number is typed in correctly or not, 
and the last digit on an ISBN number (serial numbers for books) is a
check digit. Bar codes have both parity bars (some for each digit) and 
a check digit. But how do you calculate a check digit? And what is the 
smallest check digit that provides a certain probability of catching 
an error?

A check digit can't catch all the errors. To be completely accurate 
the check would have to be the exact same size as the rest of the 
number, and thats inefficient. So if a bar code is 9 digits and there 
is one check digit, the probability of the number and size of errors 
it will catch has to do with how it's calculated.

There are many ways to calculate check digits. Credit cards use the 
Luhn code, computers use polynomial CRC values, and bar codes use a 
wide variety of different schemes:
POSTNET, Code 39, Codabar, Interleaved 2 of 5, Code 128 (sets A, B and 
C), UPC-A, EAN-13, EAN-8, EAN-128, UCC-128, MSI / Plessy, Code 11, 
RM4SCC, PLANET, 4-State, SSCC-18 and SCC-14 are just some of them!

For a math fair you could describe how the check digits are 
calculated, do some analysis to see which offers the best error 
checking ability, and so on.

Here are some Web sites with information on check digits:

   Decode the Bar Code! - Lasco Fittings   

   How UPC Bar Codes Work - HowStuffWorks   

   How To Strip Check Digit From Code 3 Of 9 Barcode Data   

   Bar Code Check Digit Calculator and Printing Application 
   for Barcode Fonts   

Or you could just search the Internet for "bar code" and "check 
digit," as I did. There are lots of sites out there!

- Doctor Jeremiah, The Math Forum   
Associated Topics:
High School Number Theory

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