Overview

This chapter is an introduction to combinational logic circuits. These are logic circuits where the output(s) depend solely on the input(s). It begins with methods of implementation of logic diagrams from Boolean expressions, the derivation of Boolean expressions from logic diagrams, input and output waveforms, and Karnaugh maps.

7.1 Implementation of Logic Diagrams from Boolean Expressions

In this section we will present procedures for converting Boolean expressions to logic diagrams using a specific type of gates or a combination of gates. The procedure is best illustrated with the examples that follow.

Important: The ANDing operation has precedence over the ORing operation. For instance, the Boolean expression AB+C implies that A must first be ANDed with B and the result must be ORed with C as shown in Figure 7.1.

Figure 7.1: Implementation of the Boolean expression AB+C

Example 7.1

Implement the complementation (inversion) operation A to A with a NAND gate, and B to B with a NOR gate.

Solution:

As shown in Figure 7.2, we can perform the inversion operation with either a NAND gate or a NOR gate by tying the inputs together.

Figure 7.2: Using NAND and NOR gates for the inversion operation