2.6: Conclusion

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Boolean algebra, or functions where the values are binary or two digit values, is the basis for the circuits that will be presented in this text. Boolean functions can always be represented in a truth table, and then translated directly into DNF. Thus any Boolean function can be written using only AND, OR, and NOT operations.

To instantiate these functions into hardware for a computer, circuits will be used. For a number of reasons, including making the circuit faster and decreasing the amount of electricity used and the amount of heat generated, it is of interest to designers to make the circuits as small as possible, and to make the circuits contain the fewest gates possible. DNF seldom represents the smallest possible circuit, and Boolean algebra is introduced as a way to simplify a circuit.

It is difficult to know if a circuit has been reduced to a minimum using just DNF, so the concept of a K-map was introduced which is a mechanical way to ensure minimum circuits.