  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.
