Exclusive-OR Representations of Boolean Functions

With the goal of making exclusive-OR formulations of switching functions more readily available to designers for implementation in LSI and VLSI technologies, we introduce the concept of an exclusive-OR space in which an exclusive-OR normal form is defined to correspond to the conventional disjunctive normal form. A geometrical representation of exclusive-OR space is described, and its various bases are listed and discussed.

[1]  Irving S. Reed,et al.  A class of multiple-error-correcting codes and the decoding scheme , 1954, Trans. IRE Prof. Group Inf. Theory.

[2]  J. Paul Roth,et al.  Computer Logic Testing And Verification , 1980 .

[3]  Jean-Pierre Deschamps,et al.  Discrete and switching functions , 1978 .

[4]  David E. Muller,et al.  Application of Boolean algebra to switching circuit design and to error detection , 1954, Trans. I R E Prof. Group Electron. Comput..

[5]  SUDHAKAR M. REDDY,et al.  Easily Testable Realizations ror Logic Functions , 1972, IEEE Transactions on Computers.

[6]  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.

[7]  George K. Papakonstantinou Minimization of Modulo-2 Sum of Products , 1979, IEEE Transactions on Computers.

[8]  Frederick F. Sellers,et al.  Error detecting logic for digital computers , 1968 .

[9]  Sudhakar M. Reddy,et al.  Fault Detecting Test Sets for Reed-Muller Canonic Networks , 1975, IEEE Transactions on Computers.

[10]  Shimon Even,et al.  On Minimal Modulo 2 Sums of Products for Switching Functions , 1966, SWAT.

[11]  John P. Robinson,et al.  A Method for Modulo-2 Minimization , 1982, IEEE Transactions on Computers.