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Description
It was the purpose of this study to develop and describe methods suitable for digital computer determination of the irredundant normal equivalents of sum-of-products form Boolean functions. The importance, meaning, and usual methods (with attendant shortcomings) of Boolean function simplification are discussed. The role of the digital computer and computer programming are briefly reviewed. Descriptions are presented of algorithms most suitable for computer determination of prime implicants and irredundant normal equivalents of the original Boolean function. The description is based on a computer program written in the NELIAC language. However, little reference is made to NELIAC in describing the program. Rather, program explanation is facilitated through the use of figures which describe, by considering specific examples, essential steps of the algorithms. The figures generally portray the manner in which information relating to Boolean terms and variables is calculated and stored within the computer memory. A description is included of the manner in which Boolean product terms (including "don't cares") of the function to be simplified are represented within the computer. Since Quine's method of iterative consensus is employed to obtain prime implicants, a method for computer determination of subsuming and consensus terms is discussed. The irredundant normal forms are obtained from Hockney's algorithm. Thus, a procedure is presented for obtaining disjoint cubes by computer determination of intersection and logical subtraction of Boolean hypercubes. The disjoint cubes define a product-of-sums form Boolean function which, when converted within the computer to an equivalent sum-of-products form, results in specification of irredundant normal equivalents of the original function.
