On the Cost of Base N Adders

The use of N-valued logics in the design of base N adder circuits is considered. Two types of N-valued logics are examined, Post N-valued logics and binary-coded N-valued logics. Specific implementations of these nonbinary logics are discussed. General formulas for the sum and carry functions of an adder are established in order to calculate the cost of base N adder stages using the Post logics. Relative costs of the base N adders using both types of N-valued logics are discussed in terms of a cost function. It is shown that for the model used, the binary-coded logics yield adders that have, in general, lower relative cost than comparabloe adders based on the Post logics, and that base 2 adders have a lower relative cost than the base N adders.