A method for simplifying Boolean functions
TL;DR: In this paper, an iterative technique for simplifying Boolean functions is presented, which enables the user to obtain prime implicants by simple operations on a set of decimal numbers which describe the function.
Abstract: This article presents an iterative technique for simplifying Boolean functions. The method enables the user to obtain prime implicants by simple operations on a set of decimal numbers which describe the function. This technique may be used for functions of any number of variables.
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TL;DR: A tabular method where the essential prime implicants are selected during the process of forming the combination tables, and other essential terms are selected from what have been described in the note as chains of selective prime implICants.
Abstract: The Quine–McCluskey method of minimizing a Boolean function gives all the prime implicants, from which the essential terms are selected by one or more cover tables known as the prime implicant tables. This note describes a tabular method where the essential prime implicants are selected during the process of forming the combination tables, and other essential terms are selected from what have been described in the note as chains of selective prime implicants. Consequently, the need for successive prime implicant tables is eliminated.
292 citations
TL;DR: A logical design theory for ternary voltage switching circuits is developed, based on familiar binary switching circuit elements and simplification methods, which leads to simple electronic realization.
Abstract: A logical design theory for ternary voltage switching circuits is developed. The theory is based on familiar binary switching circuit elements and simplification methods. The theory thus leads to simple electronic realization. The basic system of ternary switching elements consists of function realizable by means of either diode gates or a single triode (transistor). Various simplification methods for combinational circuits are described, namely a map method and two algebraic methods. The first algebraic method is an adaptation of the Quine method for determining the prime implicants of a given binary function, and the second is a modification of the Scheinman binary method.
78 citations
TL;DR: It is shown that all presented algorithms are polynomial in the number of minterms occurring in the canonical disjunctive normal form representation of a Boolean function.
54 citations
TL;DR: The method reduces the above problems into those of determining all minimal positive dependence sets, irredundant positive normal forms, and ir redundantpositive normal forms of minimal positive dependency sets, respectively, of a Boolean function f* corresponding to f.
Abstract: A new method is presented for determining all minimal dependence sets, irredundant normal forms, and irredundant normal forms of minimal dependence sets of a Boolean function f. The method reduces the above problems into those of determining all minimal positive dependence sets, irredundant positive normal forms, and irredundant positive normal forms of minimal positive dependence sets, respectively, of a Boolean function f* corresponding to f. For each problem a corresponding cover formula is developed such that the prime implicants of it are in one-to-one correspondence to all possible solutions.
46 citations
TL;DR: This note describes an iterative procedure for generating the prime implicants of switching functions by utilizing a new tabular mode of functional representation called clause-column table, which can be applied equally well to functions given in the sum-of-products or in the product- of-sums froms.
Abstract: This note describes an iterative procedure for generating the prime implicants of switching functions by utilizing a new tabular mode of functional representation called clause-column table. The procedure generates all the prime implicants and can be applied equally well to functions given in the sum-of-products or in the product-of-sums froms, both canonical and noncanonical. The procedure can also be readily adapted to determine the prime implicants of functions having a large number of unspecified or DON'T CARE terms.
23 citations
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TL;DR: A systematic procedure is presented for writing a Boolean function as a minimum sum of products and specific attention is given to terms which can be included in the function solely for the designer's convenience.
Abstract: A systematic procedure is presented for writing a Boolean function as a minimum sum of products This procedure is a simplification and extension of the method presented by W V Quine Specific attention is given to terms which can be included in the function solely for the designer's convenience
1,103 citations
01 Jan 1962
TL;DR: In this paper, the authors proposed a method of determining what they called prime implicants, and then selecting from these implicant the ''simplest normal equivalents of a formula''.
Abstract: In the application of Boolean algebra to switching circuits,1,3 one of the areas of interest is that of reduction of the functions to their simplest normal form. Quine, in formulating the special problem of simplification, proposed a method of determining what he called ?prime implicants,? and a method of selecting from the prime implicants the ?simplest normal equivalents of a formula.?4 One of the requirements of this method is that the function first be expressed in ?developed normal form? (standard sum of products or canonical form), each product of the function containing all of the letters of the function. Quine's later method eliminates this requirement.5
10 citations