Most methods for determining the prime implicants of a Boolean function depend on the minterms of the function. Deviating from this philosophy, this paper presents a method that dependson maxterms (the 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 the product of the sums is required. What is more, prime implicants can generally 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 the products 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 also hold for prime implicates. In particular, all prime implicates can be obtained from any sum of a products form.Twelve variable examples are solved to illustrate the methods.
