TR-NIS-0004 :2005.6.22

Andrzej BULLER

"S13-only" Logic

Abstract:This report provides a consideration of a logic system based exclusively on the Boolean functioh S1n, called here MEXOR, that returns 1 iff exactly one of its n arguments equals 1. Proven lemmas show how to built various Boolean functions based exclusively on 3-input MEXORs. An up-to-3-input MEXOR can be embodied as a q-cell — a square-shaped device exchanging bits with neighbor cells and returning an output value after one clock. This report presents as examples of q-cell-based circuits, flat crossing, AND-, OR-, NOR-, and NAND-gate, multiplexer, more-than-one-of-three majority function, adder, and timer.

Keywords—logic, symmetric functions, cellular arrays, pulse circuits, delay circuits