Design of Approximate Radix-4 Booth Multipliers for Error-Tolerant Computing

Approximate computing is an attractive design methodology to achieve low power, high performance (low delay) and reduced circuit complexity by relaxing the requirement of accuracy. In this paper, approximate Booth multipliers are designed based on approximate radix-4 modified Booth encoding (MBE) algorithms and a regular partial product array that employs an approximate Wallace tree. Two approximate Booth encoders are proposed and analyzed for error-tolerant computing. The error characteristics are analyzed with respect to the so-called approximation factor that is related to the inexact bit width of the Booth multipliers. Simulation results at 45 nm feature size in CMOS for delay, area and power consumption are also provided. The results show that the proposed 16-bit approximate radix-4 Booth multipliers with approximate factors of 12 and 14 are more accurate than existing approximate Booth multipliers with moderate power consumption. The proposed R4ABM2 multiplier with an approximation factor of 14 is the most efficient design when considering both power-delay product and the error metric NMED. Case studies for image processing show the validity of the proposed approximate radix-4 Booth multipliers.