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