## Math Beyond the Horizon

The Shannon expansion and BDDs

*Representing Boolean functions in a computer*

Boolean algebra deals with operations on true/false logic values, much as regular algebra deals with operations on numbers. Computers are built from circuits that perform logical operations, but can also be used to represent and manipulate functions in Boolean algebra. We will briefly discuss some of the basic properties of Boolean functions and equations, and then discuss a variety of ways in which these can be represented and manipulated in a computer. Among these is the BDD (or binary decision diagram), which is based on the Shannon expansion, a method of successively simplifying any Boolean function.

### David Hathaway

David Hathaway is a retired IBM design automation engineer and the executive director of the Vermont State Mathematics Coalition.