A novel method to simplify Boolean functions

VIshnuvajjula Charan Prasad

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.


Keywords


Boolean functions, minimization, prime implicants, prime implicates

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References


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

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