ABSTRACT
Boolean algebra unifies both logic and set theory in a very nice way. Boolean algebra plays a very important role in circuit design in computer science. It is very helpful for computer science majors to have some idea of how circuits are designed and work. This chapter begins by seeing how Boolean algebra unifies logic and set theory. It shows how to prove some of the Boolean algebra laws from the axioms given in the definition of Boolean algebra. The chapter examines the use of Boolean algebra for designing computer digital circuits. Digital circuits operate with electricity. Circuit designers need an easy way to know if different expressions really are the same thing or not. Therefore circuit designers often write expressions in one of two standardized, or canonical, ways. Every Boolean expression can be written in a sum-of-products form or in a product-of-sums form.
