TABLE OF CONTENTS The purpose of simplification of Boolean functions is to obtain an algebraic expression with less number of literals and less numbers of logic gates. This results in low-cost circuit implementation. The design procedure for combinational circuits as described in the preceding sections is intended to minimize the number of logic gates to implement a given function. This classical procedure realizes the logic circuit with fewer gates with the assumption that the circuit with fewer gates will cost less. However, in practical design, with the arrival of a variety of integrated circuits (IC), this concept is always true.
Since one single IC package contains several number of logic gates, it is economical to use as many of the gates from an already used package, even if the total number of gates is increased by doing so. Moreover, some of the interconnections among the gates in many ICs are internal to the chip and it is more economical to use such types of ICs to minimize the external interconnections or wirings among the IC pins as much as possible. A typical example of this is if the circuit diagrams of Figures 5.23 and 5.24 are considered. Both circuit diagrams perform the function of Excess-3-to-BCD code conversion and consist of 13 logic gates. However, the circuit of Figure 5.23 needs six ICs (one 3-input OR, one 3-input AND, two 2-input AND, one 2-input OR, and one INVERTER, since one 3-input OR IC package contains three gates,...
