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

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.40 no.12
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• pp.72-79
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• 2003

This paper proposes a 32${\times}$32 Modified Booth multiplier using CMOS multiple-valued logic circuits. The multiplier based on the radix-4 algorithm is designed with current mode CMOS quaternary logic circuits. Designed multiplier is reduced the transistor count by 67.1% and 37.3%, compared with that of the voltage mode binary multiplier and the previous multiple-valued logic multiplier, respectively. The multiplier is designed with a 0.35${\mu}{\textrm}{m}$ standard CMOS technology at a 3.3V supply voltage and unit current 10$mutextrm{A}$, and verified by HSPICE. The multiplier has 5.9㎱ of propagation delay time and 16.9mW of power dissipation. The performance is comparable to that of the fastest binary multiplier reported.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.15 no.7
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• pp.628-637
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• 1990

In this paper we present on architecture for a high sppeed CMOS multiplier which can be used for real-time digital signal processing. And a synthesis method for designing highly parallel algorithms in VLSI is presented. A parallel multiplier design based on the modified Booth's algorithms and Ling's algorthm. This paper addresses the design of multiplier capable of accpting data in 2's complement notation and coefficients in 2's complement notation. Multiplier consists of an interative array of sequential cells, and are well suited to VLSI implementation as a results of their modularity and regularity. Booth's decoders can be fully tested using a relatively small number af test vector.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.46 no.12
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• pp.36-42
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• 2009

This paper proposes the high-performance pipeline architecture for modified Booth multipliers. The proposed multiplier circuits are based on modified Booth algorithm and pipeline architecture which are the most widely used techniques to accelerate the multiplication speed. In order to implement the optimally pipelined multipliers, many kinds of experiments have been conducted. The experimental results show that the speed improvement gain exceeds the area penalty and this trend is manifested as the number of pipeline stages increases. It is also important to insert the pipeline registers at the proper positions. We described the proposed modified Booth multiplier circuits in Verilog HDL and synthesized the gate-level circuits using 0.13um standard cell library. The resultant multiplier circuits show better performance than others. Since they operate at GHz ranges, they can be used in the application systems requiring extremely high performance such as optical communication systems.

• The KIPS Transactions:PartA
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• v.14A no.4
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• pp.203-208
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• 2007

This paper proposes a $64{\times}64$ Modified Booth multiplier using CMOS multi-valued logic circuits. The multiplier based on the radix-4 algorithm is designed with current mode CMOS quaternary logic circuits. Designed multiplier is reduced the transistor count by 64.4% compared with the voltage mode binary multiplier. The multiplier is designed with Samsung $0.35{\mu}m$ standard CMOS process at a 3.3V supply voltage and unit current $5{\mu}m$. The validity and effectiveness are verified through the HSPICE simulation. The voltage mode binary multiplier is achieved the occupied area of $7.5{\times}9.4mm^2$, the maximum propagation delay time of 9.8ns and the average power consumption of 45.2mW. This multiplier is achieved the maximum propagation delay time of 11.9ns and the average power consumption of 49.7mW. The designed multiplier is reduced the occupied area by 42.5% compared with the voltage mode binary multiplier.

• Proceedings of the IEEK Conference
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• 2001.06a
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• pp.337-340
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• 2001

This paper presented a new structure of RSA cryptosystem using modified Montgomery algorithm and CSA(Carry Save Adder) tree. Montgomery algorithm was modified to a radix-4 modified Booth algorithm. By appling radix-4 modified Booth algorithm and CSA tree to modular multiplication, a clock cycle for modular multiplication has been reduced to (n＋3)/2 and carry propagation has been removed from the cell structure of modular multiplier. That is, the connection efficiency of full adders is enhanced.

• The Journal of the Korea institute of electronic communication sciences
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• v.19 no.2
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• pp.409-416
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• 2024

With the expansion of floating-point operation requirements for fast high-speed data signal processing and logic operations, the speed of the floating-point operation unit is the key to affect system operation. This paper studies the performance characteristics of different floating-point multiplier schemes, completes partial product compression in the form of carry and sum, and then uses a carry look-ahead adder to obtain the result. Intel Quartus II CAD tool is used for describing Verilog HDL and evaluating performance results of the floating point multipliers. Floating point multipliers are analyzed and compared based on area, speed, and power consumption. The FMAX of modified Booth encoding with Wallace tree is 33.96 Mhz, which is 2.04 times faster than the booth encoding, 1.62 times faster than the modified booth encoding, 1.04 times faster than the booth encoding with wallace tree. Furthermore, compared to modified booth encoding, the area of modified booth encoding with wallace tree is reduced by 24.88%, and power consumption of that is reduced by 2.5%.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.41 no.7
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• pp.53-61
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• 2004

In this paper, we proposed a new architecture of MAC(Multiplier-Accumulator) to operate high-speed multiplication-accumulation. We used the MBA(Modified radix-4 Booth Algorithm) which is based on the 1's complement number system, and CSA(Carry Save Adder) for addition of the partial products. During the addition of the partial product, the signed numbers with the 1's complement type after Booth encoding are converted in the 2's complement signed number in the CSA tree. Since 2-bit CLA(Carry Look-ahead Adder) was used in adding the lower bits of the partial product, the input bit width of the final adder and whole delay of the critical path were reduced. The proposed MAC was applied into the DWT(Discrete Wavelet Transform) filtering operation for JPEG2000, and it showed the possibility for the practical application. Finally we identified the improved performance according to the comparison with the previous architecture in the aspect of hardware resource and delay.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.46 no.9
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• pp.33-38
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• 2009

The group CSD (GCSD) multiplier was recently proposed based on the variation of canonic signed digit (CSD) encoding and partial product sharing. This multiplier provides an efficient design when the multiplications are performed only with a few predetermined coefficients (e.g., FFT). In many DSP applications such as FFT, the (2W-1)-bit product obtained from W-bit multiplicand and W-bit multiplier is quantized to W-bits by eliminating the (W-1) least-significant bits. This paper presents an error compensation method for a fixed-width GCSD multiplier that receives a W-bit input and produces a W-bit product. To efficiently compensate for the quantization error, the encoded signals from the GCSD multiplier are used for the generation of error compensation bias. By Synopsys simulations, it is shown that the proposed method leads to up to 84% reduction in power consumption and up to 79% reduction in area compared with the fixed-width modified Booth multiplier.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.42 no.10 s.340
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• pp.29-34
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• 2005

The maximum quantization error has serious effect on the performance of fixed-width multipliers that receive W-bit inputs and produce W-bit products. In this paper, we analyze the error bound of fixed-width modified Booth multipliers. Then, the estimation method for the number of additional columns for fixed-width multipliers is proposed to limit the maximum quantization error within a desired bound. In addition, it is shown that our methodology can be extended to reduced-width multipliers. By simulations, it is shown that the proposed error analysis method is useful to the practical design of fixed-width modified Booth multipliers.