Basic gates

Abstract

To design even simple logic circuits some techniques, or tools, will be needed. The basic tools discussed in this chapter are Boolean algebra, truth tables and Karnaugh maps (or Veitch diagrams). Boolean algebra, which is the algebra of two-state systems initially developed by George Boole, was introduced, together with truth tables, in Chapter 1. Karnaugh maps are a compact form of truth tables which provide a graphical means of obtaining an efficient logic-gate design (in this context, efficient means having the minimum number of basic gate inputs). The design process contains two basic steps: analysis, where the logic expression is defined and then converted into a truth table or a set of basic logic functions; and synthesis, where the analysed function is converted to an electronic circuit. Before discussing efficient, or minimized, circuit design, basic ways of converting truth tables to expressions and circuits will be described.