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July 1970 (vol. 19 no. 7)
pp. 627-640
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. 7, pp. 627-640, July 1970, doi:10.1109/T-C.1970.222995
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