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Multilevel Conditional Probability Estimator for Low-Power Fixed-Width Booth Multiplier

P. Gowri, N. Gunasekar, K. Mohankumar

Abstract


The occurrence of errors is inevitable in modern VLSI Technology and to overcome all possible errors is an expensive task. It not only uses a lot of power but insults the speed performance. To create an output with the same width as the input, fixed width multipliers cut short the half least significant bits (LSBs) in DSP applications. This paper proposes an accuracy adjustment fixed width booth multiplier that compensates the truncation error using a multilevel conditional probability (MLCP) estimator and derives a closed form for various bit widths L and column information. Error Tolerant Adder (ETA) circuit a little bit can reduce the strict restriction on quality of being very close to the truth to accomplish extreme improvements in both the power use and flow performance, when its compared to conventional counterparts. The proposed MLCP estimator reduces test run time and easily changes to make better quality of being very close to the truth based on mathematical derivations. The proposed MLCP uses whole non-zero code, to guess the truncation error and accomplish higher levels. What's more, the simple and small MLCP made up for circuit is proposed. The proposed MLCP booth multipliers accomplish low cost high performance.


Keywords


ETA Adder, Multilevel Conditional Probability (MLCP), High Speed, Error Tolerant.

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References


Y. H. Chen, “An Accuracy-Adjustment Fixed-Width Booth Multiplier Based on Multilevel Conditional Probability,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 23, no. 1, pp. 203-207, Jan. 2014.

K. K. Parhi, VLSI Digital Signal Processing system: Design and Implementation. New York, NY, USA: Wiley, 1999.

S. N. Tang, J. W. Tasi, and T. Y. Chang, “a 2.4-Gs/s FFT processor for OFDM-based WPAN applications,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 57, no. 6, pp. 451-455, Jun. 2010.

S. C. Hsia and S. H. Wang, “Shift-register-based data transposition for cost-effective discrete cosine transforms,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 15, no. 6, pp. 725-728, Jun. 2007.

Y. H. Chen, T. Y. Chang, and C. Y. Li, “High throughput DA-based DCT with high accuracy error-compensated adder tree,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 19, no. 4, pp. 709-714, Apr. 2011.

L. D. Van, C. C. Yang, “Generalized low-error area-efficient fixed-width multipliers,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 8, pp. 1608-1619, Aug. 2005.

L. D. Van, S. S. Wang, and W. S. Feng, “Design of the lower error fixed-width multiplier and its application,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 47, no. 10, pp. 1112-1118, Oct. 2000.

C. H. Chang, and R. K. Satzoda, “A low error and high performance multiplexer-based truncated multiplier,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 18, no. 12, pp. 1767-1771, Dec. 2010.

N. Petra, D. D. Caro, V. Garofalo, E. Napoli, and A. G. M. Strollo, “Truncated binary multipliers with variable correction and minimum mean square error,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 57, no. 6, pp. 1312-1325, Jun. 2010.

N. Petra, D. D. Caro, V. Garofalo, E. Napoli, and A. G. M. Strollo, “Design of fixed-width multipliers with linear compensation function,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 58, no. 5, pp. 947-960, May. 2011.

I. C. Wey and C. C. Wang, “Low-error and hardware-efficient fixed-width multiplier by using the dual-group minor input correction vector to lower input correction vector compensation error,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 20, no. 10, pp. 1923-1928, Oct. 2012.

S. J. Jou, M. H. Tsai, and Y. L. Tsao, “Low-error reduced-width booth multipliers for DSP applications,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 50, no. 11, pp. 1470-1474, Nov. 2003.

H. A. Huang, Y. C. Liao, and H. C. Chang, “A self-compensation fixed-width booth multiplier and its 128-point FFT applications,” in Proc. IEEE Int. Symp. Circuits Syst., May 2006, pp. 3538-3541.

Y. H. Chen and T. Y. Chang, and R. Y. Jou, “A statistical error-compensated Booth multiplier and its DCT applications,” in Proc. IEEE Region 10 Conf., Nov. 2010, pp. 1146-1149.

T. B. Junag and S. F. Hsiao, “Low-error carry-free fixed-width multipliers with low-cost compensation circuits,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 52, no. 6, pp. 299-303, Jun. 2005.

K. J. Cho, K. C. Lee, J. G. Chung, and K. K. Parhi, “Design of low-error fixed-width modified booth multiplier,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 12, no. 5, pp. 522-531, May. 2004.

S. R. Kuang, J. P. Wang, and C. Y. Guo, “ Modified booth multipliers with a regular partial product array,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 56, no. 5, pp. 404-408, May. 2009.

Y. H. Chen, C. Y. Li, and T. Y. Chang, “Area-effective and power-efficient fixed-width booth multipliers using generalized probabilistic estimation bias,” IEEE J. Emerging Sel. Topics Circuits Syst., vol. 1, no. 3, pp. 277-288, Sep. 2011.

J. P. Wang, S. R. Kunag, and S. C. Liang, “High-accuracy fixed-width modified booth multipliers for lossy applications,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 19, no. 1, pp. 52-60, Jan. 2011.

C. Y. Li, Y. H. Chen, T. Y. Chang, and J. N. Chen, “A probabilistic estimation bias circuit for fixed-width booth multiplier and its DCT applications,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 58, no. 4, pp. 215-219, Apr. 2011.

Y. H. Chen and T. Y. Chang, “A high-accuracy adaptive conditional- probability estimator for fixed-width booth multipliers,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 59, no. 3, pp. 594-603, Mar. 2012.

B. Parhami, Computer Arithmetic: Algorithms and Hardware Design. Oxford, U.K.: Oxford Univ. Press, 2000.

C. H. Chang, J. Gu, and M. Zhang, “Ultra low-voltage low-power CMOS 4-2 and 5-2 compressors for fast arithmetic circuits,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 51, no. 10, pp. 1985-1997, Oct. 2004.


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