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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. 479485
ASCII Text  x  
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. 479485, May, 1972.  
BibTex  x  
@article{ 10.1109/TC.1972.223544, author = {S.Y.H. Su and A.A. Sarris}, title = {The Relationship Between Multivalued Switching Algebra and Boolean Algebra Under Different Definitions of Complement}, journal ={IEEE Transactions on Computers}, volume = {21}, number = {5}, issn = {00189340}, year = {1972}, pages = {479485}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1972.223544}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  The Relationship Between Multivalued Switching Algebra and Boolean Algebra Under Different Definitions of Complement IS  5 SN  00189340 SP479 EP485 EPD  479485 A1  S.Y.H. Su, A1  A.A. Sarris, PY  1972 KW  Algebraic method of minimization KW  Boolean algebra KW  combinational circuits KW  definition of complement KW  multivalued logic KW  multivalued switching functions KW  Nvalued switching logic KW  switching algebra. VL  21 JA  IEEE Transactions on Computers ER   
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, Nvalued 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. 479485, May 1972, doi:10.1109/TC.1972.223544
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