Hybrid Low Radix Encoding-Based Approximate Booth Multipliers

Radix-4 Booth encoding provides ease in the generation of partial products, thus is widely used to achieve power-efficient and low-area signed multipliers. Conversely, the radix-8 Booth encoding exhibits low-performance as it requires generation of odd multiples of the multiplicand. In this brief, this issue is addressed by approximating the odd multiples of radix-8 to their nearest power of two such that the errors complement each other. In the pursuit of an accuracy-energy trade-off, hybrid low radix (HLR) based two approximate Booth multipliers (HLR-BM1 and HLR-BM2) are designed. HLR-BM2, compared to the previous best error-optimized design (ABM1), achieved a reduced energy of 22% with a comparable MRED. Moreover, HLR-BM2 achieves an improvement of 75% in MRED and 11% in energy consumption compared to the previously best energy-optimized design (RAD64). As a case study, performance for image transformation is evaluated. A high peak signal-to-noise ratio (PSNR, close to 50dB) is obtained for the proposed multiplier designs.