Multiple Valued Logic: Concepts and Representations

Miller, David M.; Thornton, Mitchell A.

doi:10.2200/s00065ed1v01y200709dcs012

Cited by 86 publications

(74 citation statements)

References 55 publications

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“…2. The Min function is used to compare the minimum among the several literals [3]. A representation of a quaternary switching function that is analogous (but not identical) to the binary sum of minterms representation can be formulated using the Max function in place of the binary inclusive OR function and product terms may be formed using the Min function in place of the binary AND operation.…”

Section: A Min and Max Gatementioning

confidence: 99%

“…3 and Fig. 4, Forward cycle or mod-sum and reverse cycle or mod-difference are cycle gates where the output varies taking the reference point as one input and varying with respect to the quaternary value of the other input [3]. In case of forward cycle gate, with respect to one reference point the movement of the input quaternary value is clockwise and in case of reverse gate it is anticlockwise.…”

Section: International Journal Of Computermentioning

confidence: 99%

“…Quaternary states {0, 1, 2, 3} with a set of operators and axioms are used to define quaternary algebra. Each of the quaternary states {0, 1, 2, 3} has its two bits binary equivalents 00 (absolute low), 01 (intermediate low), 10 (intermediate high) and 11 (absolute high) and each of the quaternary bits is called 'qudit' [3], [7], when expressed in numbers. The logic values can also be indicated by two binary digits 'a1' and 'a0', respectively which is inscribed and packed together using the following notion A={a1, a0} where the term '2a1 + a0' denotes the magnitude of the variable 'A' in decimal system [4].…”

Section: Quaternary Algebramentioning

confidence: 99%

“…In many applications, that is why, it is imperative that the operators of the algebra have simple and efficient circuit implementations for reducing circuit complexity. Although functions like max, min, cycle gate (forward and reverse cycle), successor and predecessor, 2 nd level successor and predecessor have already been introduced [3], [4], yet, no specifications to the truth table, logic diagram and corresponding equations have been stated so far abating the process of further implementation of these functions in complex circuitry. The paper proposes the techniques for finding the truth table, logic diagram and the equation for some consequential functional operators like max, min, cycle gate (forward and reverse cycle), successor and predecessor, 2 nd level successor and predecessor which can be further implemented to solve circuit complexity.…”

Section: Proposed Ideamentioning

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%

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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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Section: A Min and Max Gatementioning

confidence: 99%

Section: International Journal Of Computermentioning

confidence: 99%

Section: Quaternary Algebramentioning

confidence: 99%

Section: Proposed Ideamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Logic Design of Elementary Functional Operators in Quaternary Algebra

Faiyaz¹,

Chowdhury²,

Ishtiak³

2016

IJCTE

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Remote Sensing Imagery Spatial Resolution Enhancement

Stankevich

Piestova

Lubskyi

2021

Recognition and Perception of Images

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Looking Beyond 0 and 1: Principles and Technology of Multi‐Valued Logic Devices

et al. 2022

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Figure 8. Single-electron transistors (SETs). a) Schematic structure and b) transfer I-V characteristic of a typical SET. c) Schematic diagram and scanning electron microscopy image of the two-gate SET. d) Transfer I-V characteristic of the two-gate SET at V in2 = 0 V and 0.2 V. c,d) Reproduced with permission. [18] Copyright 2000, IEEE. e) Circuit diagram of the universal literal gate and its periodic V in −V out characteristic. Reproduced with permission. [98] Copyright 2003, IEEE. f) Schematic of the two-input hybrid MOSFET-SET device. g) The output voltage as a function of two input gate voltages. f,g) Adapted with permission. [103] Copyright 2009, IEEE. h,i) Schematic diagram of the Si EQD SET (h) and its typical two-peak transfer characteristic (i). j) Contour plot demonstrating I D as a function of V DS and V G enabling ternary and quaternary operation regimes. h-j) Reproduced with permission. [105]

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Multiple Valued Logic: Concepts and Representations

Cited by 86 publications

References 55 publications

Logic Design of Elementary Functional Operators in Quaternary Algebra

Logic Design of Elementary Functional Operators in Quaternary Algebra

Remote Sensing Imagery Spatial Resolution Enhancement

Looking Beyond 0 and 1: Principles and Technology of Multi‐Valued Logic Devices

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