Recently, highly-efficient two-step recoded and one-step nonrecoded trinary signed-digit (TSD) carry-free adder/subtracter has been presented based on redundant bit representation (RBR) for the operands digits where it has been shown that only 24 (30) minterms are needed to implement the two-step recoded TSD (the one-step nonrecoded) addition for any operand length. In this paper, we present four different multiplication designs based on our proposed recoded and nonrecoded TSD adders. Our multiplication designs require a small number of reduced minterms to generate the multiplication partial products.
