• Journal of the Korean Institute of Telematics and Electronics
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• v.15 no.5
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• pp.29-33
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• 1978

In this paper, the properties of Galois fields defined over any finite field are analysed to derive Galois switching functions and the arithmetic operation methods over any finite field are showed. The polynomial expansions over finite fields by Lagrange's interpolation method are derived and proved. The results are applied to multivalued single variable logic networks.

• Journal of IKEEE
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• v.7 no.2 s.13
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• pp.135-143
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• 2003

This paper describes the design techniques of the data converters for Multiple-Valued Logic(MVL). A 3.3V low power 4 digit CMOS analog to quaternary converter (AQC) and quaternary to analog converter (QAC) mainly designed with the neuron MOS down literal circuit block has been introduced. The neuron MOS down literal architecture allows the designed AQC and QAC to accept analog and 4 level voltage inputs, and enables the proposed circuits to have the multi-threshold properity. Low power consumption of the AQC and QAC are achieved by utilizing the proposed architecture.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.44 no.2
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• pp.104-112
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• 2007

We developed a $7{\times}7$ parallel multiplier using LTPS-TFT. The proposed multiplier has multi-valued logic 7-3 Compressor with folding, 3-2 Compressor, and final carry propagation adder. Architecture minimized the carry propagation. And power consumption reduced by switching the current source to the circuit which is operated in current mode. The proposed multiplier improved PDP by 23%, EDP by 59%, and propagation delay time by 47% compared with Wallace Tree multiplier.

• Proceedings of the Korea Multimedia Society Conference
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• 2002.11b
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• pp.587-592
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• 2002

본 논문에서는 De Bruijn 그래프에 기초한 다중처리기구성의 한 가지 방법을 제안하였다. 제안한 방법에서는 유한체상의 수학적 성질과 그래프의 성질을 사용하여 변환연산자를 제한하였으며, 이들 변환연산자를 이용하여 De Bruijn 그래프의 변환표를 도출하였다. 그리고, 이 변환표로부터 유한체상의 De Bruijn 그래프를 도출하였다. 제안한 다중처리기는 유한체상의 임의의 소수와 양의 정수에 대해 구성할 수 있으며 고장허용컴퓨팅시스템, 파이프라인 시스템, 병렬처리 네트워크, 스위칭 함수와 이의 회로, 차세대 디지털논리시스템 및 컴퓨터구조 중의 하나인 다치디지털논리시스템 등에 적용할 수 있으리라 전망된다.

• The KIPS Transactions:PartA
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• v.11A no.2
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• pp.115-122
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• 2004

In this paper, the multiple-valued adders and multipliers are implemented by current-mode CMOS. First, we implement the 3-valued T-gate and the 4-valued T-gate using current-mode CMOS which have an effective availability of integrated circuit design. Second we implement the circuits to be realized 2-variable 3-valued addition table and multiplication table over finite fields $GF(3^2)$, and 2-variable 4-valued addition table and multiplication table over finite fields $GF(4^2)$ with the multiple-valued T-gates. Finally, these operation circuits are simulated under $1.5\mutextrm{m}$ CMOS standard technology, $15\mutextrm{A}$ unit current, and 3.3V VDD voltage Spice. The simulation results have shown the satisfying current characteristics. The 3-valued adder and multiplier, and the 4-valued adder and multiplier implemented by current-mode CMOS is simple and regular for wire routing and possesses the property of modularity with cell array. Also, since it is expansible for the addition and multiplication of two polynomials in the finite field with very large m, it is suitable for VLSI implementation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.5
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• pp.411-421
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• 1988

This paper offers a method to design CCD four-valued circuits using the tabular method. First, the four-valued logic function is decomposed by hand-calculation or computer program. Nest, the algorithm is derived form the tabular method based on the decomposition process to realize the DDC four-valued circuit. According to this algorithm, the two-variable four valued logic function is decomposed and realized by CCD network with four basic gates. The synthesis method in this paper proves that the number of devices and cost is considerably reduces as compared with the existing methods to realize the same logic functions.

• Journal of Advanced Navigation Technology
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• v.16 no.1
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• pp.62-69
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• 2012

Multiple-control Toffoli(MCT) gates are macro-level multiple-valued gates needing quantum technology dependent primitive gates, and have been used in Galois Field sum-of-product (GFSOP) based synthesis of quantum logic circuit. Reversible logic is very important in quantum computing for low-power circuit design. This paper presents a reversible GF4 multiplier at first, and GF4 multiplier based quaternary MCT gate realization is also proposed. In the comparisons of MCT gate realization, we show the proposed MCT gate can reduce considerably primitive gates and delays in contrast to the composite one of the smaller MCT gates in proportion to the multiple-control input increase.

• Journal of IKEEE
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• v.9 no.1 s.16
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• pp.1-6
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• 2005

This paper proposes a high performance multiplier using CMOS multiple-valued logic circuits. The multiplier based on the Modified Baugh-Wooley algorithm is designed with current-mode CMOS quaternary logic circuits. The multiplier is functionally partitioned into the following major sections: partial product generator block(binary-quaternary logic conversion block), current-mode quaternary logic full-adder block, and quaternary-binary logic conversion block. The proposed multiplier has 4.5ns of propagation delay and 6.1mW of power consumption. This multiplier can easily adapted to the binary system by the encoder and the decoder. This circuit is designed with 0.35um standard CMOS process at 3.3V supply voltage and 5uA unit current. The validity and effectiveness are verified through the HSPICE simulation.

• Journal of IKEEE
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• v.10 no.2 s.19
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• pp.128-133
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• 2006

This paper describes a high speed interface circuit using redundant multi-valued logic for high speed communication ICs. This circuit is composed of encoding circuit that serial binary data are received and converted into parallel redundant multi-valued data, and decoding circuit that converts redundant multi-valued data to parallel binary data. Because of the multi-valued data conversion, this circuit makes it possible to achieve higher operating speeds than that of a conventional binary logic. Using this logic, the proposed 1:4 DEMUX (demultiplexer, serial-parallel converter), was designed using a 0.35um standard CMOS technology. Proposed DEMUX is achieved an operating speed of 4.5Gb/s with a supply voltage of 3.3V and with power consumption of 53mW. The operating speed of this circuit is limited by the maximum frequency which the 0.35um process has. Therefore, this circuit is to achieve CMOS communication ICs with an operating speed greater than 10Gb/s in submicron process of high operating frequency.

• The Transactions of the Korea Information Processing Society
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• v.4 no.7
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• pp.1851-1864
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• 1997

This paper presents an algorithm simplifying the ESOP function by several rules. The algorithm is repeatedly performing operations based on the state of each terms by the product transformation operation of two functions and thus it is simplifying the ESOP function through the reduction of the product terms. Through the minimization of the product terms of the multi-valued input binary multi-output function, an optimization of the input has been done using EXOR PLA with input decoder. The algorithm when applied to four valued arithmetic circuit has been used for a EXOR logic circuit design and the two bits input decoder has been used for a EXOR-PLA design. It has been found from a computer simulation(IBM PC486) that the suggested algorithm can reduce the product terms of the output function remarkably regardless of the number of input variables when the variable AND-EXOR PLA is applied to the poperation circuit.