3-VALUED QUASI-LINEAR TRANSFORMATION FOR LOGIC SYNTHESIS

A nonlinear transformation, called the sign transform, is defined and studied. It maps all the ternary functions onto themselves, is uniquel y invertible and is inherently related to Walsh and Walsh-Galois trans forms. Decomposable Boolean functions and ternary product terms are ma pped analytically into the sign domain. It is shown that sign coeffici ents describe the structure of a ternary output logic network implemen ted by a complete basis: EXOR of variables and sign function. Methods are discussed for direct transformation of switching functions without having to use the butterfly algorithm: Shannon's decomposition in the sign domain and, in general, merging sign spectra of subfunctions.