### Quality of Minimal Sets of Prime Implicants of Boolean Functions

#### Abstract

Two new problems are posed and solved concerning minimal sets of prime implicants of Boolean functions. It is well known that the prime implicant set used to realize a Boolean function with logic gates should be minimal and have as few literals as possible. But it is not well known that min term repetitions should also be as few as possible to reduce power consumption. Determination of minimal sets of prime implicants is a well known problem. But nothing is known on the *least number* of (i) prime implicants (ii) literals and (iii) min term repetitions , *any minimal set* of prime implicants will have. These measures are useful to assess the *quality* of a minimal set. They are then extended to determine least number of prime implicants / implicates required to design a static hazard free circuit. The new technique tends to give smallest set of prime implicants for various objectives.

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