Hybrid Partial Product-Based High-Performance Approximate Recursive Multipliers

Approximate recursive multipliers exhibit low-power operation because they are designed using smaller power-efficient approximate multiplier blocks. These building blocks can be configured by varying the approximation levels for a wide range of larger multiplier sizes. However, most of the building blocks proposed for recursive multipliers are either slightly inaccurate or hardware-efficient with limited accuracy. In this brief, hybrid partial product-based building blocks are proposed by considering the probability distribution of the input operands. An efficient hardware implementation of approximate 4×4 multipliers is achieved, while maintaining the required accuracy. Moreover, high-performance approximate NOR-based half adder (NxHA) and full adder (NxFA) cells are proposed for use in a 4×4 multiplier. Three different strategies (Ax8-1/2/3) are further proposed and analyzed for utilizing the 4×4 multipliers when designing larger multipliers. Ax8-2 provides the best trade-off among the designs with a moderate MRED. A reduction of 30 and 17 percent in the MRED is achieved compared to previous best energy-optimized and MRED-optimized designs. Among the designs with higher MREDs, Ax8-3 exhibits the smallest MRED and PDP. Moreover, it shows an improvement of 7 to 28 percent in delay compared to existing approximate recursive designs. As a case study, image multiplication is evaluated; a high peak signal-to-noise ratio (PSNR) with a value close to 50dB is obtained for the proposed multiplier designs.