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Dynamic Error-Compensated Fixed-Width Booth Multiplier Based on Conditional-Probability of Input Series

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Abstract

This paper proposes a dynamic error-compensated circuit for a fixed-width Booth multiplier based on the conditional probability of input series (CPIS), which enables high-speed operation and low circuit overhead. The dynamic compensated value is produced directly from the multiplier of input series simultaneously with the Booth encoder and therefore does not affect the critical path. The compensated formula is derived using a mathematical probability model, rather than time-consuming simulation. This formula is a function of bit-length of the multiplier; thus, the compensated circuit is easily implemented for bit-length of 32, 64, or longer. Accuracy-efficiency, which indicates the signal-to-noise ratio per unit area and unit delay, is included for ease of comparison. Compared with previous works, the greatest advantage of the proposed CPIS is high speed. Furthermore, the proposed CPIS achieves higher accuracy-efficiency. Implemented using the TSMC 0.18-\(\upmu \)m CMOS process, the proposed 32-bit Booth multiplier has an operation frequency of 50 MHz with power consumption of 7.3 mW.

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Acknowledgments

The authors would like to thank the National Chip Implementation Center (CIC), Taiwan, for providing the standard cell and electronic design automation tools.

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Authors and Affiliations

  1. Electronics Engineering Department and Institute of Electronics, National Chiao Tung University, Hsinchu, 300, Taiwan

    Wen-Quan He & Shyh-Jye Jou

  2. Department of Electronic Engineering, Chang Gung University, Tao-Yuan, 333, Taiwan

    Yuan-Ho Chen

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  1. Wen-Quan He
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  2. Yuan-Ho Chen
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  3. Shyh-Jye Jou
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Correspondence to Yuan-Ho Chen.

Additional information

This work was supported in part by the Ministry of Science and Technology, Chip implementation Center, and Chang Gung University under Project Number MOST 104-2221-E-182 -079, CIC T18-102D-E0031, and UERPD2E0051, respectively.

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He, WQ., Chen, YH. & Jou, SJ. Dynamic Error-Compensated Fixed-Width Booth Multiplier Based on Conditional-Probability of Input Series. Circuits Syst Signal Process 35, 2972–2991 (2016). https://doi.org/10.1007/s00034-015-0186-2

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  • DOI: https://doi.org/10.1007/s00034-015-0186-2

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