Abstract :
This paper describes a new approach to the design of combinational logic using large-scale integrated (LSI) circuit technology. A simple "prototype" logic function of n binary variables is imbedded within an array of at most (n+1) rows and columns. The cells of this array contain two-input EXCLUSIVE-OR gates, and its rows are fed by the input variables and logical "1." Its column outputs are first-degree polynomial functions of the input variables. These functions supply inputs to, and modify the output of, the prototype in order to realize the desired function. These transformations form a group; specifically, the largest subgroup of the (n+1)-dimensional affine group such that input variable encodings are not affected by feedback from the function\´s output.
Keywords :
Affine group, combinational logic, equivalence classes, Fourier transform, large-scale integration, switching theory.; Combinational circuits; Encoding; Input variables; Integrated circuit technology; Large scale integration; Logic arrays; Logic design; Logic functions; Polynomials; Prototypes; Affine group, combinational logic, equivalence classes, Fourier transform, large-scale integration, switching theory.;
