  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.
