1. MAT 1000 Mathematics in Today's World Winter 2015

2. Today We will look at more identification numbers and barcodes.

3. Codabars The codabar scheme detects 100% of single digit errors, and 98% of most other common errors. It is used by all major credit card companies, as well as blood banks, and some libraries. It can be used with ID numbers of various lengths. Credit card numbers are 16 digits long. The last digit is a check digit.

4. Codabars

11. The ISBN-10 Coding System Is it possible to have a coding system which catches 100% of single digit errors and 100% of transposition errors? Yes. The coding system used for books, called the ISBN-10 system does this. ISBN-10 numbers have 10 digits. The last digit is the check digit.

12. The ISBN-10 Coding System

19. Bar Codes Written numerals can be hard for an electronic scanner. Machines have an easier time reading black and white stripes. A bar code is a series of dark bars and light spaces that encodes a number.

20. ZIP Code Bar Codes Encode ZIP codes as a series of long and short bars. Each digit is encoded by 5 bars. In each block of 5 bars, two are long and three are short. Long “guard bars” start and end the bar code.

22. ZIP+4 Codes ZIP+4 is a 9-digit system with more detailed address information. These are encoded the same way, with longer bar codes. The tenth digit is a check digit.

24. UPC Bar Codes UPC bar codes are similar to ZIP code bar codes. Instead of short and long bars, the information is carried in the widths of the bars and spaces. This works well with supermarket optical scanners. What if you scan an item backwards? The UPC bar codes use different patterns for the first half and the second half.