Binary full adder, made of fusion gates, in sub-excitable Belousov-Zhabotinsky system

Abstract

A sub-excitable BZ medium responds to asymmetric local perturbation by producing travelling localised excitation wave-fragments, distant relatives of dissipative solitons. The size and life span of an excitation wave-fragment depend on the illumination level of the medium. Under the right conditions the wave-fragments conserve their shape and velocity vectors for extended time periods. We interpret the wave-fragments as values of Boolean variables. When two or more wave-fragments collide they annihilate or merge into a new wave-fragment. States of the logic variables, represented by the wave-fragments, are changed in the result of the collision between the wave-fragments. Thus, a logical gate is implemented. Several theoretical designs and experimental laboratory implementations of Boolean logic gates have been proposed in the past but little has been done cascading the gates into binary arithmetical circuits. We propose a unique design of a binary one-bit full adder based on a fusion gate. A fusion gate is a two-input three-output logical device which calculates conjunction of the input variables and conjunction of one input variable with negation of another input variable. The gate is made of three channels: two channels cross each other at an angle, third channel starts at the junction. The channels contain BZ medium. When two excitation wave-fragments, travelling towards each other along input channels, collide at the junction they merge into a single wave-front travelling along the third channel. If there is just one wave-front in the input channel, the front continues its propagation undisturbed. We make a one-bit full adder by cascading two fusion gates. We show how to cascade the adder blocks into a many-bit full adder. We evaluate feasibility of our designs by simulating evolution of excitation in the gates and adders using numerical integration of Oregonator equations.