Applicability of Partial Ternary Full Adder in Ternary Arithmetic Units

This paper explores whether or not a complete ternary full adder, whose input variables can independently be '0', '1', or '2', is indispensable in the arithmetic blocks of adder, subtractor, and multiplier. Our investigations show that none of the mentioned arithmetic units require a complete ternary full adder. Instead, they can be designed by use of partial ternary full adder, whose input carry never becomes '2'. Furthermore, some new ternary compressors are proposed in this paper without the requirement of complete ternary full adder. The usage of partial ternary full adder can help circuit designers to simplify their designs, especially in transistor level.