Clause-Column Table Approach for Generating All the Prime Implicants of Switching Functions

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.

[1]  Willard Van Orman Quine,et al.  The Problem of Simplifying Truth Functions , 1952 .

[2]  E. W. Veitch,et al.  A chart method for simplifying truth functions , 1952, ACM '52.

[3]  M. Karnaugh The map method for synthesis of combinational logic circuits , 1953, Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics.

[4]  Willard Van Orman Quine,et al.  A Way to Simplify Truth Functions , 1955 .

[5]  Raymond J. Nelson,et al.  Weak simplest normal truth functions , 1955, Journal of Symbolic Logic.

[6]  Raymond J. Nelson,et al.  Simplest normal truth functions , 1955, Journal of Symbolic Logic.

[7]  E. McCluskey Minimization of Boolean functions , 1956 .

[8]  W. Quine On Cores and Prime Implicants of Truth Functions , 1959 .

[9]  E. McCluskey Minimal sums for boolean functions having many unspecified fundamental products , 1962 .

[10]  Insley B. Pyne,et al.  The Reduction of Redundancy in Solving Prime Implicant Tables , 1962, IRE Trans. Electron. Comput..

[11]  A. Mukhopadhyay,et al.  A method of determination of all the minimal forms of Boolean functions , 1962 .

[12]  M. S. Basu,et al.  A Mechanized Chart for Simplification of Switching Functions , 1962, IRE Trans. Electron. Comput..

[13]  Frank B. Hall Boolean prime implicants by the binary sieve method , 1962, Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics.

[14]  A. Scheinman A method for simplifying Boolean functions , 1962 .

[15]  S. R. Das,et al.  Maxterm Type Expressions of Switching Functions and Their Prime Implicants , 1965, IEEE Trans. Electron. Comput..

[16]  Edward J. McCluskey,et al.  Introduction to the theory of switching circuits , 1965 .

[17]  Ananta Choudhury,et al.  Simplification of Switching Functions Involving a very Large Number of ‘Don't Care’ States† , 1966 .

[18]  Richard C. T. Lee,et al.  A New Algorithm for Generating Prime Implicants , 1970, IEEE Transactions on Computers.

[19]  S. R. Das,et al.  An Approach for Simplifying Switching Functions by Utilizing the Cover Table Representation , 1971, IEEE Transactions on Computers.

[20]  S. R. Das Comments on "A New Algorithm for Generating Prime Implicants" , 1971, IEEE Trans. Computers.