Analog and threshold building blocks for variable-radix adders and other logic

A system of “TKM” logic, based on 3-state threshold devices, Kirchoff adders (i.e., summing amplifiers), and linear amplifiers is proposed. It is shown that TKM logic can realize any multiple-valued truth table, and that the length of the alphabet of truth values may be arbitrary. This logic is shown to be particularly well suited to the synthesis of variable-radix adders, in which alterations of the radix are obtained by adjustments of the gain or attenuation of one or more amplifiers. When TKM is used in conjunction with a proposed “symmetric analog coding” for the representation of numbers, the generation of r-1 complements and, as a consequence, the execution of r-ary subtraction and division, are facilitated. It is conjectured that the feasibility of variable-radix adders is a step toward the realization of adaptive computation at the hardware level.