Left-to-right carry-free scheme for computing ab+cd

A radix-4 scheme is proposed for computing the sum of products s=ab+cd using left-to-right multipliers and on-the-fly conversion. The final result is obtained without the extra delay of a carry-propagate adder in conventional schemes. The inputs and the output are in the two´s complement fired-point representation. The most-significant part of the result can also be used the most-significant digit first to allow overlap with successive operations. The scheme can be used to compute ab+c if d=1 and a(b+c) if d=a. The critical path is kept small by the use of redundant arithmetic. The proposed algorithm, its implementation and performance are discussed.