n × n carry-save multipliers without final addition

Carry-save multipliers require an adder at the last step to convert the carry-sum representation of the most significant half of the result into an irredundant form. A multiplication scheme where by this conversion is performed with a circuit operating in parallel with the carry-save array is presented. The resulting implementation, when a radix-2 adder array is used, produces a result on 2n bits with a delay comparable to that of the multiplier proposed by M.D. Ercegovac and T. Lang (1990). When a radix-4 array is used, the proposed unit is almost twice as fast as units proposed previously