Datawidth-aware energy-efficient multipliers: a case for going sign magnitude

Algorithms from many application domains, such as linear algebra and image/signal processing, heavily use the multiplication operator. Despite hardware support which is present in most modern cores, multiplication remains one of the most energy hungry arithmetic operations. This work explores how the energy efficiency of hardware multipliers can be improved by taking into account that the operands of a multiplication typically do not utilize the full width of the datapath. Seven datawidth-aware multiplier designs are implemented and evaluated. Post-layout energy analysis is performed to obtain the energy efficiency of each design for a number of representative benchmarks targeting the consumer market. The results show a significant improvement in energy efficiency compared to a 32-bit Baugh-Wooley baseline multiplier. A 32-bit sign-magnitude based design, integrated in a two's complement datapath, is shown to have a 1.38 times better energy efficiency than a baseline two's complement multiplier. In the best case (JPEG encoding), the energy efficiency is increased by a factor 2.25, demonstrating that a sign-magnitude multiplier, and datawidth-aware multipliers in general, are an attractive option for ultra low-energy designs.