The Radix-2^m Squared Multiplier

Abstract

Multipliers are present in a large variety of applications. However, it is usually responsible for most of the power dissipation. On the other hand, the squared multiplier is a particular case of the general-purpose multiplier, in which both operands are the same, proportioning many architecture optimizations. This paper introduces the radix-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> squared array multiplier architecture. Our architecture proposal for the squared multiplier is the first to reduces the partial products by splitting the operands into mbit groups. Our squared multiplier architecture explores different adder schemes in the multipliers adder tree. As a case study, we demonstrate our squared multiplier proposal for m=2 (radix-4). We investigated the Wallace and Dadda addition trees employing as final carry propagating adder (CPA) the Ripple Carry adder (RCA) and with the adder automatically selected by the synthesis tool. Our best radix-4 squared multiplier proposal employs the Dadda technique and the RCA to implement the adder tree, showing significant energy savings of 20.5%, 56.5%, and 47.4%, for 8, 16, and 32 bits, respectively, compared to the squared multiplier automatically selected by the synthesis tool. Furthermore, our best radix-4 squared multiplier proposal outperforms the Vedic squared multiplier with energy savings in about 21.5%, 71.0%, and 9.0%, respectively, for 8, 16, and 32 bits.