Symmetric Logic Synthesis with Phase Assignment

Decomposition of any Boolean Function BFn of n binary inputs into an optimal inverter coupled network of Symmetric Boolean functions SFk (k ≤ n) is described. Each SF component is implemented by Threshold Logic Cells, forming a complete and compact T -Cell Library. Optimal phase assignment of input polarities maximizes local symmetries. Rank spectrum is a new BFn description independent of input ordering, obtained by mapping its minterms onto an othogonal n×n grid of (transistor-) switched conductive paths, minimizing crossings in the silicon plane. Using this ortho-grid structure for the layout of SFk cells, without mapping to T -cells, yields better area efficiency, exploiting the maximal logic path sharing in SF ’s. Results obtained with a CAD tool ”Ortolog” based on these concepts, are reported. Relaxing symmetricto planarBoolean functions is sketched, to improve lowsymmetry BF decomposition.