On Half-Adders Based on Fusion of Signal Carriers: Excitation, Fluidics, and Electricity

Likely outcomes of a collision between two objects are annihilation, reflection, or fusion. We show how to construct a one-bit adder with patterns that fuse on impact. A fusion gate has two inputs and three outputs. When a signal is generated on a single input, the object propagates along its own output trajectory. When both inputs are active, the objects collide at a junction of input trajectories, fuse, and propagate along a dedicated output trajectory. Thus two outputs produce conjunction of one signal with negation of another signal, and the third output produces conjunction of input signals. By merging two outputs in one, we make a one-bit half-adder: one output is the conjunction of input signals; another output is the exclusive disjunction of the signals. We discuss blueprints of the half-adders realized with two types of physical signal carriers—wave fragments in excitable mediumand high-velocity jet streams. We also propose an electrical circuit analogous to a fusion half-adder. By running fusion half-adders in reverse, we find that despite realizing the same functions when in a straight mode, all devices implement different functions when their inputs are swapped with outputs.