Issue No. 07 - July (1970 vol. 19)

ISSN: 0018-9340

pp: 627-640

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.

INDEX TERMS

Affine group, combinational logic, equivalence classes, Fourier transform, large-scale integration, switching theory.

CITATION

R.J. Lechner, "A Transform Approach to Logic Design",

*IEEE Transactions on Computers*, vol. 19, no. , pp. 627-640, July 1970, doi:10.1109/T-C.1970.222995