Post algebras and ternary adders

Abstract

Except for qubits for which the different possible values are unordered, the different values of m-valued circuits either with voltage levels, current levels or charge levels are totally ordered. Either at the Math level (Post algebras) or at the circuit level, it means that each multiple valued level must be decomposed into binary levels, processed with binary computation and finally converted into a multiple valued level. Using ternary adders as example, we show that the ternary-to-binary decoding and binary encoding should be applied to the whole adder or to restricted parts of the adder. The second approach using multiplexers leads to the most efficient ternary adders. However, a comparison with binary adders shows that the ternary-to-binary and binary-to-ternary conversions is the reason for which the binary adders are more efficient.