Boolean Algebra and Its Applications (Dover Books on Computer Science) by J. Eldon Whitesitt

Author:J. Eldon Whitesitt [Whitesitt, J. Eldon]
Language: eng
Format: epub, mobi
ISBN: 0486477673
Amazon: B00GHQVQ04
Publisher: Dover Publications
Published: 2012-05-23T21:00:00+00:00

FIGURE 4–6

Two problems inherent in any simplification procedure should be mentioned at the outset. First, it may be difficult, or impossible, to tell from the Boolean function alone which of several circuits is “simplest.” The best circuit may well depend on the relative cost of wiring and of various types of switches required by the several equal functions which may be written. The final simplification, then, depends upon the specifications for a given circuit.

Another difficulty is that the simplest, or most economical, circuit may not be a series-parallel circuit. Since Boolean algebra reflects this type of circuit only, the final simplification may often be performed by the designer who recognizes such a possibility. In this step, Boolean algebra is of no help. Two kinds of circuits in which the series-parallel circuit is not the best form are discussed in later sections. For the time being, we will omit any such considerations.

In using the basic laws of Boolean algebra, it often happens that a possible simplification is overlooked. It may happen that a certain step is easier to recognize if stated in terms of one of the dual laws rather than in terms of the other. This suggests another method of simplification which may help. To simplify a function f, the dual of f may be taken and the resulting expression simplified. If the dual is taken again, the function f is obtained in a different form. This will usually be simpler than the original.

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