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Radix-8 Modified Booth Fixed-Width Signed Multipliers with Error Compensation

  • Research Article-Electrical Engineering
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Abstract

The Booth multipliers require lower number of addition operations compared to the traditional multipliers. Further, higher radix Booth multiplier requires lesser number of adders in its circuit implementation. Multiply and accumulate (MAC) unit plays a crucial role in digital signal processing circuits. Handling the data in area-efficient MAC circuits is challenging since the data word length closely doubles on each multiplication. The data path of higher word length possesses higher hardware complexity. However, such hardware complexity can be minimized by deploying the fixed-width multipliers (FWM) in MAC circuits. In FWMs, the multiplication result of \({{X}_{L-\mathrm{bits}}}\times {{Y}_{L-\mathrm{bits}}}\) is rounded to the higher significant L bits by truncating the rest of lower significant bits. Nevertheless, this truncation introduces the error in multiplication result. This paper presents a radix-8 Booth-based fixed-width signed multipliers with error compensation. Moreover, the estimation of bias value for the error compensation in radix-8 Booth FWM is presented. Accuracy of the fixed-width multiplication with the proposed compensation is analyzed. In addition, the multiplier circuits based on the proposed methods are designed and implemented and the experimental results are discussed.

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Authors and Affiliations

  1. Department of Electronics and Communication Engineering, GMR Institute of Technology, Rajam, Andhra Pradesh, India

    Govinda Rao Locharla

  2. Department of Electronics and Communication Engineering, National Institute of Technology, Rourkela, Odisha, India

    Kamala Kanta Mahapatra & Samit Ari

Authors
  1. Govinda Rao Locharla
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  2. Kamala Kanta Mahapatra
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  3. Samit Ari
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Correspondence to Govinda Rao Locharla.

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Locharla, G.R., Mahapatra, K.K. & Ari, S. Radix-8 Modified Booth Fixed-Width Signed Multipliers with Error Compensation. Arab J Sci Eng 46, 1115–1125 (2021). https://doi.org/10.1007/s13369-020-04920-w

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  • DOI: https://doi.org/10.1007/s13369-020-04920-w

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