Identification Numbers and Modular Arithmetic
The first topic we will investigate is the mathematics of identification numbers. Many familiar things are described by a code of digits; zip codes, items in a grocery store, and books, to name three. One feature to all of these codes is the inclusion of an extra numerical digit, called a check digit, designed to detect errors in reading the code. When a machine (or a human) reads information, there is always the possibility of the information being read incorrectly. For example, moisture or dirt on the scanner used by a grocery store clerk can prevent an item’s code from being read correctly. It would be unacceptable if, because of a scanning error, customers were charged for caviar when they are buying tuna fish. The use of the check digit allows for the detection of some scanning errors. If an error is detected, the item is re-scanned until the correct code is read.