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 http://www.lascofittings.com/BarCode-EDI/Decode.htm How UPC Bar Codes Work - HowStuffWorks http://www.howstuffworks.com/upc.htm How To Strip Check Digit From Code 3 Of 9 Barcode Data http://www.pixtran.com/support/kb/1113.shtml Bar Code Check Digit Calculator and Printing Application for Barcode Fonts http://www.bizfonts.com/barcodeapp/ 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 http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.