Method for Designing Efficient Mixed Radix Multipliers

The multiplication of two signed inputs, \(A {\times } B\) , can be accelerated by using the iterative Booth algorithm. Although high radix multipliers require summing a smaller number of partial products, and consume less power, its performance is restricted by the generation of the required hard multiples of B ( \(\pm \phi B\) terms). Mixed radix architectures are presented herein as a method to exploit the use of several radices. In order to implement efficient multipliers, we propose to overlap the computation of the \(\pm \phi B\) terms for higher radices with the addition of the partial products associated to lower radices. Two approaches are presented which have different advantages, namely a combinatory design and a synchronous design. The best solutions for the combinatory mixed radix multiplier for \(64\times 64\) bits require \(8.78\) and \(6.55~\%\) less area and delay in comparison to its counterpart radix-4 multiplier, whereas the synchronous solution for \(64\times 64\) bits is almost \(4{\times }\) smaller in comparison with the combinatory solution, although at the cost of about \(5.3{\times }\) slowdown. Moreover, we propose to extend this technique to further improve the multipliers for residue number systems. Experimental results demonstrate that best proposed modulo \(2^{n}{-}1\) and \(2^{n}{+}1\) multiplier designs for the same width, \(64{\times }64\) bits, provide an Area-Delay-Product similar for the case of the combinatory approach and \(20~\%\) reduction for the synchronous design, when compared to their respective counterpart radix-4 solutions.