A Review of Boolean Algebra

This chapter begins with the underlying concepts of crisp logic, deals with the definition of an algebra or algebraic system and reviews the fundamentals of Boolean algebra. It argues that the entries in truth a table are called minterms and that a minterm is a binary aggregate of logical 0s and 1s that sets the logical value, true or false, of single cell entries in truth tables. The chapter utilizes the Karnaugh map (K-map) as a special arrangement of a truth table. The K-Map can be used for manipulating both crisp and fuzzy logic expressions. As a further addition to the K-Map, the concept of don't care variables was introduced. Such variables are determined to never occur in an input pattern and thus can be entered into a K-Map and used to help simplify the logic yet never affect the state of the system's logical output.