A TRANSFORM FOR LOGIC NETWORKS

The transform presented in this paper applies to functions which describe logic network behavior. Given a function G defined over a finite domain, it is shown that G(u)=∑tF(t)ut for each element u in the domain, where finite-field arithmetic is assumed. Here, function F is the transform of G, and it is shown that F(t) = ∑u G(u)(-u)-t for each integer t in a finite set. Both form and development of this transform pair resembles the Fourier transform in harmonic analysis. The above expansion for G leads directly to a logic network synthesis of G. Networks so derived are composed of multioutput modules suitable for integrated-circuit fabrication. Expansions can be simplified to yield networks requiring fewer modules. Applications in the paper illustrate the use of the polynomial expansion for synthesis of a set of switching functions, and of a sequential network required in a radar coding digital system. The transform also serves as a test for linear switching functions. Development of the finite transform employs Galois field arithmetic. Necessary background material is included in the paper to permit a self-contained presentation of all results. Copyright © 1969 by The Institute of Electrical and Electronics Engineers, Inc.