Development of a novel quaternary algebra with the design of some useful logic blocks

Jahangir, Ifat; Hasan, Dihan; Islam, Shajid; Siddique, Nahian; Hasan, Md. Mehedi

doi:10.1109/iccit.2009.5407140

Cited by 13 publications

(11 citation statements)

References 7 publications

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“…Proposed quaternary full adder designed with unique encoding technique [6]. Power dissipation of full adder using unique encoding in CMOS technique is 3.6261 x 10 -6 watt.…”

Section: Quaternary Full Addermentioning

confidence: 99%

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Power Optimization of Combinational Quaternary Logic Circuits

Kanchan¹

2015

IJRITCC

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Abstract-Due to the need of interconnections design of binary circuits is limited. Interconnection increases area, delay and energy consumption in CMOS digital circuits. A possible solution could be here as, in the same chip area we use more sets of signals. Multiple value logic can decrease average power required for level transitions and reduces the number of necessary interconnections. In this paper we design various combinational modules using Quaternary logic. Various combinational circuits are Quaternary full adder using unique encoding, quaternary encoder & decoder and quaternary multiplexer. These designs are aimed to reduce the transistors used in the implementation of circuits and reducing the power dissipation. Power optimization is achieved using MTCMOS technique. Simulation has been done in Tanner 13 EDA tool on BSIM3 180nm CMOS technology.Keywords-Multi value logic, power optimization, quaternary full adder, quaternary encoder & decoder, quaternary multiplexer and MTCMOS technique.

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“…Proposed quaternary full adder designed with unique encoding technique [6]. Power dissipation of full adder using unique encoding in CMOS technique is 3.6261 x 10 -6 watt.…”

Section: Quaternary Full Addermentioning

confidence: 99%

“…In the field of computing, multiple value logic can lead to significant improvement because of its higher information capacity and required fewer blocks of circuits per symbol as compared to binary systems [6].…”

Section: Introductionmentioning

confidence: 99%

Power Optimization of Combinational Quaternary Logic Circuits

Kanchan¹

2015

IJRITCC

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Section: Quaternary Algebramentioning

confidence: 99%

“…That is why it is prerequisite to express its fundamental operators in terms of equations and logic diagram for further implementation in multiplex algorithms. In this paper, we have designed some important functions like max, min, mod-sum, mod-difference, successor, predecessor, 2 nd level successor or predecessor and 3 rd level successor and predecessor using earlier proposed logic functions and basic operators proposed in [3]- [6] which can be implemented subsequently in composite circuits.…”

Section: Introductionmentioning

confidence: 99%

“…If the transposition of position of bits changes the corresponding binary value then they are known as asymmetrical. Intermediate states (1, 2) are asymmetrical as interchanging the binary equivalents changes the quaternary state 1 to 2 and vice versa [6].Quaternary algebra is in congruence with binary logic in terms of the basic operators like OR, AND, BUFFER, BASIC INVERTER, XOR, BASIC NAND, BASIC NOR and BASIC XNOR and that is why the interfacing of binary to quaternary can easily be conducted by just using an encoder. So, quaternary algebra can be used as models for the initial design of logic circuits whether they are implemented with MVL signal levels or binary after being encoded.…”

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confidence: 99%

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Logic Design of Elementary Functional Operators in Quaternary Algebra

Faiyaz¹,

Chowdhury²,

Ishtiak³

2016

IJCTE

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Abstract-Multivalued logic is an extension of Boolean algebra with high radix approaches and is preferable over conventional binary logic operations for reduction in interconnection cost, chip area both on-chip and between chips and high information handing capability. This paper includes the design of elementary combinational quaternary operators that have sufficient representative capability to efficiently implement in intricate quaternary arithmetic circuits. Design of several combinational logic circuits have been presented which can function individually and in logic blocks for designing further complex circuits resulting in a reduction of circuit complexity and better speed processing in integrated circuit technology.Index Terms-Cycle gate, max and min gate, multivalued logic, quaternary algebra. I. INTRODUCTIONBinary logic has been predominant in embedded system and a fundamental for computer programming and mathematical logic due to its easy accessibility and widespread use in logic circuits. Operating with binary logic implies to controlling the real world with computers and that an alternative improved approach with a better usage of transmission path, storage and processing of large amount of information in digital signal processing even exist seems somewhat impossible. Yet, Moore's law states that, the number of transistors on integrated circuits doubles approximately every two years. As this law has been by far proven accurate, it is high time we considered alternative approaches to reduce this tremendous positive rate of elements used in integrated circuits. It has been suggested that by increasing the processing speed, memory capacity, sensors or memory states, this significant rate can be inhibited to an exponential rate. But, due to the inherent limitation data representation system of only two distinct levels {0, 1}, binary logic impedes the scope for multiple states and lacks high speed and information handling capacity. On the other hand, multivalued number systems, such as ternary and quaternary systems with a radix more than '2' (p>2) emerges with the immediate benefit of larger information handling and storage capacities.Multivalued logic system introduces new operators in addition to binary values {0, 1} and is a proposed extension of the idea that n valued logic can be used instead of two logical values (that is, true or false, logic high or low) where n>2 [1].Perhaps one of the most tangible immediate benefits of Manuscript received September 9, 2014; revised January 5, 2015.The authors were with the Ahsanullah University of Science and Technology, Dhaka, Bangladesh (e-mail: asif.faiyaz@gmail.com).higher-radix approaches like quaternary logic lies in their potential for reduction of the wiring congestion and interconnection cost [2]. Using a single conductor to transmit three or more discrete voltage or current values allows for greater information content per wire and thus results in a circuit with reduced conductors and logic gates than the binary-valued counterpart. Furthermore model...

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All-optical quaternary logic gates – An extension of binary logic gates

Garai¹

2015

Optics & Laser Technology

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Development of a novel quaternary algebra with the design of some useful logic blocks

Cited by 13 publications

References 7 publications

Power Optimization of Combinational Quaternary Logic Circuits

Power Optimization of Combinational Quaternary Logic Circuits

Logic Design of Elementary Functional Operators in Quaternary Algebra

All-optical quaternary logic gates – An extension of binary logic gates

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