### A novel method to simplify Boolean functions

#### Abstract

Most methods for the determination of prime implicants of a Boolean function depend on minterms of the function. Deviating from this philosophy, this paper presents a method which depends on maxterms ( minterms of the complement of the function) for this purpose. Normally maxterms are used to get prime implicates and not prime implicants. It is shown that **all** prime implicants of a Boolean function can be obtained by expanding and simplifying **any** product of sums form of the function appropriately. No special form of product of sums is required. More generally prime implicants can be generated from **any form** of the function by converting it into a POS using well known techniques. The prime implicants of a product of Boolean functions can be obtained from the prime implicants of individual Boolean functions. This allows us to handle big functions by breaking them into product of smaller functions. A simple method is presented to obtain one minimal set of prime implicants from all prime implicants without using minterms. Similar statements hold for prime implicates also . In particular **all** prime implicates can be obtained from **any** sum of products form. Twelve variable examples are solved to illustrate the methods.

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DOI: https://doi.org/10.7494/automat.2018.22.2.29

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