• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.6 no.2
• /
• pp.323-329
• /
• 2002

This paper describes an efficient error-compensation technique for designing a low-error truncated Booth multiplier which produces an N-bit output from a two's complement multiplication of two N bit inputs by eliminating the N least-significant bits. Applying the proposed method, a truncated Booth multiplier for area-efficient and low-power applications has been designed, and its performance(truncation error, area) was analyzed. Since the truncated Booth multiplier does not have about half the partial product generators and adders, it results an area reduction of about 35％, compared with no-truncated parallel multipliers. Error analysis shows that the proposed approach reduces the average truncation error by approximately 60％, compared with conventional methods. A 16-b$\times$16-b truncated Booth multiplier core is designed on full-custom style using 0.35-${\mu}{\textrm}{m}$ CMOS technology. It has 3,000 transistors on an area of 330-${\mu}{\textrm}{m}$$\times$262-${\mu}{\textrm}{m}$ and 20-㎽ power dissipation at 3.3-V supply with 200-MHz operating frequency.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2001.10a
• /
• pp.617-620
• /
• 2001

This paper describes an efficient error-compensation technique for designing a low-error truncated Booth multiplier that receives two N-bit numbers and produces an N-bit product by eliminating the N least-significant bits. Applying the proposed method, a truncated Booth multiplier for area-efficient and low-power applications has been designed, and its performance (truncation error, area) was analyzed. Since the truncated Booth multiplier omits about half the partial product generators and adders, it has an area reduction by about 35%~40%, compared with non-truncated parallel multipliers. Error analysis shows that the proposed approach reduces the average truncation error by approximately 30%~40%, compared with conventional methods.

• IEMEK Journal of Embedded Systems and Applications
• /
• v.15 no.5
• /
• pp.235-242
• /
• 2020

This paper analyzes the effect of reduced output width of the truncated logarithmic multiplication and application to inferences using convolutional neural networks (CNNs). For small hardware overhead, output width is reduced in the truncated Mitchell multiplier, so that fractional bits in multiplication output are minimized in error-resilient applications. This analysis shows that when reducing output width in the truncated Mitchell multiplier, even though worst-case relative error increases, average relative error can be kept small. When adopting 8 fractional bits in multiplication output in the evaluations, there is no significant performance degradation in target CNNs compared to existing exact and original Mitchell multipliers.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.11 no.3
• /
• pp.563-569
• /
• 2007

As the mobile communication and the semiconductor technology is improved continuously, mobile contents such as the multimedia service and the 2D/3D graphics which require high level graphics are serviced recently. Mobile chips should consume small die area and low power. In this paper, we design a truncated floating-point multiplier that is useful for the 2D/3D vector graphics in mobile devices. The truncated multiplier is based on the radix-4 Booth's encoding algorithm and a truncation algorithm is used to achieve small area and low power. The average percent error of the multiplier is as small as 0.00003% and neglectable for mobile applications. The synthesis result using 0.35um CMOS cell library shows that the number of gates for the truncated multiplier is only 33.8 percent of the conventional radix-4 Booth's multiplier.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.37 no.9
• /
• pp.55-65
• /
• 2000

In this paper, we propose a hardware reduced multiplier for DSP applications. In many DSP applications, all of multiplier products were not used, but only upper bits of product were used. Kidambi proposed truncated unsigned multiplier for this idea. in this paper, we adopt this scheme to Booth multiplier which can be used real DSP systems. Also, zero input guarantees zero output that was not provided in previous paper. In addition, we propose bit extension scheme to reduce truncation error more and more. And, we adopted this multiplier to FIR filters for more efficient design.

• Proceedings of the IEEK Conference
• /
• 1998.10a
• /
• pp.1085-1088
• /
• 1998

In this paper, we propose a hardware reduced multiplier for DSP applications. In many DSP application, all of multiplier products were not used, but only upper bits of rpoduct were used. Kidambi proposed truncated unsigned multiplier for this idea. In this paper, we abopt this scheme to Booth multiplier which can be used for real DSP systems. Also, zero input guarantees zero output that was not provided in the previous work.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.37 no.11
• /
• pp.85-95
• /
• 2000

FIR digital filter is one of important blocks in DSP application. For more effective operation, lots of architecture are proposed. In our paper, we proposed a high speed FIR filter with area efficiency. To fast operation, we used transposed form filter as basic architecute. And, we used dual path registers line to wupport variation of filter operation, and filter cascade is also considered. To reduce area, we adopted truncated Booth multiplier to our filter design. As a result, we showed that filter area is reduced when filter optimization using of dual path registers line and truncated multiplier with same constraints againt previous method.

• Proceedings of the Korean Society of Broadcast Engineers Conference
• /
• 2015.11a
• /
• pp.108-109
• /
• 2015

본 논문은 low-rank 행렬의 truncated nuclear norm 최소화를 이용한 HDR (high dynamic range) 영상 합성 기법을 제안한다. 제안하는 기법에서는 기존의 LDR (low dynamic range) 영상에서 얻은 밝기의 선형 관계에 기반하여 HDR 합성을 low-rank 행렬 완성 문제로 변환한 후, ALM (augmented Lagrange multiplier) 기법을 이용하여 효율적으로 최적의 해를 구한다. 컴퓨터 모의실험을 통해 제안하는 기법이 기존 기법에 비해서 낮은 계산 복잡도를 보이면서도 더 높은 품질의 HDR 영상을 합성하는 것을 확인한다.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.29 no.2C
• /
• pp.298-305
• /
• 2004

This paper presents an error compensation method for a fixed-width modified Booth multiplier that receives a W-bit input and produces a W-bit product. To efficiently compensate for the quantization error, Booth encoder outputs (not multiplier coefficients) are used for the generation of error compensation bias. The truncated bits are divided into two groups depending upon their effects on the quantization error. Then, different error compensation methods are applied to each group. By simulations, it is shown that quantization error can be reduced up to 50％ by the proposed error compensation method compared with the existing method with approximately the same hardware overhead in the bias generation circuit. It is also shown that the proposed method leads to up to 40％ reduction in area and power consumption of a multiplier compared with the ideal multiplier.

• ETRI Journal
• /
• v.43 no.4
• /
• pp.684-693
• /
• 2021

This paper presents a low-cost two-stage approximate multiplier for bfloat16 (brain floating-point) data processing. For cost-efficient approximate multiplication, the first stage implements Mitchell's algorithm that performs the approximate multiplication using only two adders. The second stage adopts the exact multiplication to compensate for the error from the first stage by multiplying error terms and adding its truncated result to the final output. In our design, the low-cost multiplications in both stages can reduce hardware costs significantly and provide low relative errors by compensating for the error from the first stage. We apply our approximate multiplier to the convolutional neural network (CNN) inferences, which shows small accuracy drops with well-known pre-trained models for the ImageNet database. Therefore, our design allows low-cost CNN inference systems with high test accuracy.