• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.8C
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• pp.832-837
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• 2005

This paper presents a design method for fixed-width squarer that receives a W-bit input and produces a W-bit squared product. To efficiently compensate for the quantization error, modified Booth encoder signals (not multiplier coefficients) are used for the generation of error compensation bias. The truncated bits are divided into two groups (major/minor group) depending upon their effects on the quantization error. Then, different error compensation methods are applied to each group. By simulations, it is shown that the performance of the proposed method is close to that of the rounding method and much better than that of the truncation method and conventional method. It is also shown that the proposed method leads to up to $28\%\;and\;27\%$ reduction in area and power consumption compared with the ideal squarers, respectively.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.12
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• pp.31-38
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• 2010

In tins paper, a new DA(Distributed Arithmetic) tilter implementation technique has been proposed. Contrary to vertical directional calculation of input sample bit format in the conventional DA implementation technique, proposed implementation technique utilizes horizontal directional calculation of input sample bit format. Since proposed technique calculates in horizontal direction, it does not need ROM and utilizes the Modified Booth algorithm. Furthermore proposed technique can be applied to implement the variable coefficients filters in addition to the fixed coefficients filters. Using conventional and proposed techniques, a 20 tap filter is implemented by Verilog-HDL coding. Through Synopsis synthesis tool, it has been shown that 41.6% area reduction can be achieved.

• Proceedings of the IEEK Conference
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• 2000.06b
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• pp.145-148
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• 2000

A 16bit asynchronous multiplier has been designed using micropipelind structure with 2 phase and data bundling. And 4-radix modified Booth algorithm, CPlatch(Cature-Pass latch) and modified 4-2 counters have adopted in this design. It is implemented in 0.65$\mu\textrm{m}$ double-poly/double-metal CMOS technology by using 12,074 transistors with core size of 1.4${\times}$1.8$\textrm{mm}^2$. And our design results in a computation rate 55MHz a supply voltage of 3.3V.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.1025-1028
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• 1998

Hardware to implement the parallelized Floating-point rounding algorithm is described. For parallelized additions, we propose an addition module which has carry selection logic to generate two results accoring to the input valuse. A multiplication module for parallelized multiplications is also proposed to generate Sum and Carry bits as intermediate results. Since these modules process data in IEEE standard Floatingpoint double precision format, they are designed for 53-bit significands including hidden bits. Multiplication module is designed with a Booth multiplier and an array multiplier.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.38 no.3
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• pp.51-51
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• 2001

본 논문에서는 CMOS 로직과 pass-transistor logic(PTL)의 장점만을 가진 새로운 복합모드로직(Compound Mode Logic)을 제안하였다. 제안된 로직은 VLSI설계에서 중요하게 부각되고 있는 저전력, 고속 동작이 가능하며 실제로 전가산기를 설계하여 측정 한 결과 복합모드 로직의 power-delay 곱은 일반적인 CMOS로직에 비해 약 22% 개선되었다 제안한 복합모드 로직을 이용하여 고성능 32×32-bit 곱셈기를 설계 제작하였다. 본 논문의 곱셈기는 개선된 사인선택(Sign Select) Booth 인코더, 4-2 및 9-2 압축기로 구성된 데이터 압축 블록, 그리고 carry 생성 블록을 분리한 64-bit 조건 합 가산기로 구성되어 있다. 0.6um 1-poly 3-metal CMOS 공정을 이용하여 제작된 32×32-bit 곱셈기는 28,732개의 트랜지스터와 1.59×l.68 ㎜2의 면적을 가졌다. 측정 결과 32×32-bit 곱셈기의 곱셈시간은 9.8㎱ 이었으며, 3.3V 전원 전압에서 186㎽의 전력 소모를 하였다.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.34C no.10
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• pp.27-35
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• 1997

In this paper, we propose a new scheme for the generation of partial products for VLSI fast parallel multiplier. It adopts a new encoding method which halves the number of partial products using 2x2 submultipliers and rearrangement of primitive partial products. The true 4-input CSA can be achieved with appropriate rearrangement of primitive partial products out of 2x2 submultipliers using the newly proposed theorem on binary number system. A 16bit x 16bit multiplier has been desinged using the proposed method and simulated to prove that the method has comparable speed and area compared to booth's encoding method. Much smaller and faster multiplier could be obtained with far optimization. The proposed scheme can be easily extended to multipliers with inputs of higher resolutions.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.10
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• pp.67-72
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• 1994

In this paper we suggest a 32 bit high speed parallel multiplier which plays an important role in digital signal processing. We employ a bit-pair recoding Booth algoritham that gurantees n/2 partial product terms, which uniformly handles the signed-operand case. While partial product terms are generated, a special method is suggested to reduce time delay by employing 1's complement instead of 2's complement. Later when partial products are added, the additional 1 bit's are packed in a single partial product term and added to in the parallel counter. Then 16 partial product terms are reduced to two summands by using successive parallel counters. Final multiplication value is obtained by a BLC adder. When this multiplier is simulated under 0.8$\mu$CMOS standard cell we obtain 30ns multiplier speed.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.5
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• pp.71-80
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• 1995

The usual approach for desinging a fast multiplier involves finding a way to quickly add up all the partial products, based on parital product recoding scheme and carry-save addition. This paper describes theoretical medels for area and time complexities of Multibit Reconding Paralle Multiplier (MRPM), which is a generalization of the modified Booth recoding scheme. Based on the proposed models, time performance, hardware requirements and area-time efficiency are analyzed in order to determine optimal recoding size for very large scale integration (VLSI) realization of the MRPM. Some simulation results show that the MRPM with large multiplier and multiplicand size has optimal area-time efficiency at the recoding size of 4-bit.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.2
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• pp.452-456
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• 2010

Multiplication is a fundamental arithmetic operation in many digital signal processing (DSP) and communication algorithms. The group CSD (GCSD) multiplier was recently proposed based on the variation of canonical 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 this paper, it is shown that, by exploiting the characteristics of the filter coefficients, GCSD multipliers can be used for the efficient implementation of time-multiplexed FIR filters.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.2A
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• pp.129-136
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• 2005

A multiplier generator, VPM_Gen (Variable-Precision Multiplier Generator), which generates Verilog-HDL models of multiplier cores with user-defined bit-width specification, is described. The bit-widths of operands are parameterized in the range of $8-bit{\sim}32-bit$ with 1-bit step, and the product from multiplier core can be truncated in the range of $8-bit{\sim}64-bit$ with 2-bit step, resulting that the VPM_Gen can generate 3,455 multiplier cores. In the case of truncating multiplier output, by eliminating the circuits corresponding to the truncation part, the gate counts and power dissipation can be reduced by about 40% and 30%, respectively, compared with full-precision multiplier. As a result, an area-efficient and low-power multiplier core can be obtained. To minimize truncation error, an adaptive error-compensation method considering the number of truncation bits is employed. The multiplier cores generated by VPM_Gen have been verified using Xilinx FFGA board and logic analyzer.