Design Of Approximate Booth Multipliers For Error-tolerant Computing

Approximate computing is a new approach to design low power and high performance circuits that are used in error-tolerant applications including multimedia,image processing and pattern recognition,in which approximate computing can produce useful results at the cost of precision.In this paper,approximate radix-4 Booth multiplication is proposed by using the concept of approximate computing.The accurate modified radix-4 Booth multiplication is analyzed in this paper which is divided into three parts: the radix-4 Booth encoding,the partial product reduction using compressors and the fast addition.The approximate designs are proposed for the Booth encoder and the compressor.ABE-1,ABE-2 and ABE-3 are three approximate radix-4 Booth encoding designs which are based on the modified Booth encoder.The approximate Booth encoders can reduce the hardware resources signif icantly with low error rate occurring compared with the accurate Booth encoder.Meanwhile,the approximate regular partial product array is proposed to make the array more regular and reduce the compressor count.This array design can reduce one compression stage and the critical path of the multiplication compared with the accurate array.An approximate 4-2 compressor is illustrated and used in the approximate Booth multiplication des ign.The approximate factor p is the width of approximate bits which the approximate encoders and compressors are used in.Hardware and error figures of the proposed approximate multiplication are analyzed in different case of p.Compared to the accurate multiplier,the approximate one has better performance on power consumption,delay and area.While considering the hardware and error figures,the proposed approximate radix-4 Booth multipliers have better performance over the other existing approximate Booth multipliers.The proposed approximate multipliers and the existing approximate multipliers are also applied into the image processing and FIR filter processing.The proposed approximate multipliers show better reliability and practicability by comparing with the SNRs of the output signals.The combination of the design and application analysis shows that the reliability and practicability of the proposed approximate Booth multier is promising in error-tolerant computing.