Numerical codes, such as ISBN numbers on books or the UPC code on other packaged goods, are ubiquitous in the marketplace. Nearly all of these codes come with a special number, called the check digit, whose purpose is to prevent the codes from being incorrectly processed. We will explain the mathematics behind the design of some of these check digit protocols and see how they are capable of detecting (or not detecting) certain kinds of errors. In a few years the publishing industry will convert to a new ISBN check digit protocol, and we will see why the error-detecting capability of the new system is in a sense worse than the current version!

Prior experience with modular arithmetic will be helpful, but in any case it will be explained as needed through examples.