Switching Circuits, Proofs, and Logic

Abstract

The two-element set plays a vital role in computer science, both as the bits 0 and 1 of binary arithmetic (corresponding to the two stable states of the basic subcomponents of computer circuitry), and as the two truth values, T (true) and F (false), of the logical analysis of circuitry, and the tests of programs. Section 4.1 introduces the basic operations of negation, conjunction, and disjunction on truth values, and shows how these operations can be used to express Boolean functions in normal form. We briefly discuss the use of components corresponding to these basic operations in building up computer circuits for addition. Section 4.2 looks at proof techniques from two perspectives. The first makes explicit the various “everyday” techniques we use in proving theorems in this book. The second gives a formal discussion of the notion of proof in propositional logic, and closes with a brief introduction to the quantifiers of predicate logic.