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  • 1972
  • Issue No. 5 - May
  • Abstract - The Relationship Between Multivalued Switching Algebra and Boolean Algebra Under Different Definitions of Complement
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The Relationship Between Multivalued Switching Algebra and Boolean Algebra Under Different Definitions of Complement
May 1972 (vol. 21 no. 5)
pp. 479-485
S.Y.H. Su, Department of Electrical Engineering, University of Southern California
The relationship between multivalued switching algebra and Boolean algebra is presented by introducing different definitions for the complements of multivalued variables. For every definition introduced, the paper points out which Boolean algebra theorems are valid for multivalued cases, which are invalid, and gives proofs to substantiate the claim. It is shown that DeMorgan's theorem holds for all four definitions of complement given in this paper. One definition allows us to map the multivalued variables into binary variables. Under this definition, all axioms and theorems of Boolean algebra are satisfied and can be used for minimization of any multivalued switching function f. Illustrative examples for minimizing f and its complement f are given.
Index Terms:
Algebraic method of minimization, Boolean algebra, combinational circuits, definition of complement, multivalued logic, multivalued switching functions, N-valued switching logic, switching algebra.
Citation:
S.Y.H. Su, A.A. Sarris, "The Relationship Between Multivalued Switching Algebra and Boolean Algebra Under Different Definitions of Complement," IEEE Transactions on Computers, vol. 21, no. 5, pp. 479-485, May 1972, doi:10.1109/T-C.1972.223544
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