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Journal ArticleDOI

New Decomposition Theorems on Majority Logic for Low-Delay Adder Designs in Quantum Dot Cellular Automata

TL;DR: The design of low-delay multibit adders in quantum dot cellular automata is considered and a general approach for delay reduction based on two new theorems called decomposition theorem is presented.
Abstract: The design of low-delay multibit adders in quantum dot cellular automata is considered in this brief. We present a general approach for delay reduction based on two new theorems called decomposition theorems. We consider the carry-lookahead adder (CLA) and the carry-flow adder (CFA) as specific applications of the theorems. For 16-bit CLA and 16-bit CFA, the decomposition theorems yield reductions in delay for the leading carry of approximately 60% and 25%, respectively, when compared to the best existing designs. In addition, the decomposition theorems lead to designs with low area-delay product. Simulations in QCADesigner are also presented.
Citations
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Journal ArticleDOI
TL;DR: A coplanar QCA crossover architecture in the design of QCA full adders is used that leads to reduction ofQCA cell count and area consumption without any latency penalty and further investigates the impact of these gains on carry flow QCA adders.
Abstract: We use a coplanar QCA crossover architecture in the design of QCA full adders that leads to reduction of QCA cell count and area consumption without any latency penalty. This crossover uses non-adjacent clock zones for the two crossing wires. We further investigate the impact of these gains on carry flow QCA adders. These designs have been realized with QCADesigner, evaluated, and tested for correctness. For better performance comparison with previous relevant works, we use a QCA-specific cost function, as well as the conventional evaluation method. We show 23% cell count and 48% area improvements over the best previous QCA full adder design. Similar results for 4-, 8-, 16-, 32-, and 64-bit adders are 29% (22%), 24% (51%), 19% (54%), 13% (69%), and 9% (49%) cell count reduction (less area consumption), respectively.

197 citations


Cites background or methods from "New Decomposition Theorems on Major..."

  • ...[28] V. Pudi and K. Sridharan, “New decomposition theorems on majority logic for low-delay adder designs in quantum dot cellular automata,” IEEE Trans....

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  • ...Regarding [28], the information required by the cost function is not available....

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  • ...[8] V. Pudi and K. Sridharan, “Low complexity design of ripple carry and Brent–Kung adders in QCA,” IEEE Trans....

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  • ...However, Pudi and Sridharan [28] have efficiently used QMs in realizing group generate signals, as is reproduced and justified in Eqn....

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Journal ArticleDOI
TL;DR: A new special low-complexity QCA 4:1 multiplexer, which is application-specific to the proposed ALU, and a new QCA full adder is proposed based on the cell interaction, which outperform in comparison to counterpart designs in terms of cell number, area, latency, and power consumption.
Abstract: Quantum-dot cellular automata (QCA) is a new nano-scale technology that due to making significant improvements in the design of electronic circuits can be considered as an appropriate alternative to CMOS technology. The arithmetic logic unit (ALU) is a fundamental component of the central processing unit to carry out the arithmetic and logical operations that multiplexer and full adder play an important role in its operations. In this brief, based on the extracted features of the arithmetic operations of the ALU, we propose a new special low-complexity QCA 4:1 multiplexer, which is application-specific to the proposed ALU. Moreover, a new QCA full adder is proposed based on the cell interaction. Likewise, a QCA multilayer ALU structure is designed based on the validated proposed structures to carry out four logical and eight arithmetic operations. The functional correctness of the proposed structures are evaluated by QCADesigner tool; also, QCAPro as an accurate power estimator tool is applied to investigate their power dissipation. The simulation results demonstrate that the proposed structures outperform in comparison to counterpart designs in terms of cell number, area, latency, and power consumption.

76 citations


Cites background or methods from "New Decomposition Theorems on Major..."

  • ...In addition, there are several ways to cross the wires on each other such as single-layer crossing, multilayer crossing, and logical crossing [2]....

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  • ...The four-zone plan, which is known as Landauer clocking is the most common scheme that is applied in QCA technology that includes Relax, Switch, Hold, and Release phases [2]....

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Journal ArticleDOI
TL;DR: A detailed comparative study reveals that the proposed QCA adder not only offers significantly high degree of fault-tolerance but also performs fairly well as compared to the existing adders with respect to other design metrics too, thereby ensures practical realizability of the proposed adder.

67 citations

Journal ArticleDOI
TL;DR: The simulation results demonstrate that the proposed QCA multiplexer architectures have the best performance in terms of clock delay, circuit complexity, and area in comparison with other QCAmultiplexing architectures.
Abstract: The quantum-dot cellular automata (QCA) technology is a promising alternative technology to CMOS technology to extend the exponential Moore's law progress of microelectronics at nanoscale level, which is expected to be beneficial for digital circuits. This paper presents and evaluates three multiplexer architectures: a new and efficient 2:1 multiplexer architecture, a 4:1 multiplexer architecture, and 8:1 multiplexer architecture in the QCA technology. The 4:1 and 8:1 QCA multiplexer architectures are proposed based on the 2:1 QCA multiplexer. The proposed architectures are implemented with the coplanar crossover approach. These architectures are simulated using the QCADesigner tool version 2.0.1. The 2:1, 4:1, and 8:1 QCA multiplexer architectures utilize 15, 107, and 293 cells, respectively. The simulation results demonstrate that the proposed QCA multiplexer architectures have the best performance in terms of clock delay, circuit complexity, and area in comparison with other QCA multiplexer architectures.

64 citations

Journal ArticleDOI
TL;DR: A new adder is proposed that outperforms all state-of-the-art competitors and achieves the best area-delay tradeoff and is obtained by using an overall area similar to the cheaper designs known in literature.
Abstract: As transistors decrease in size more and more of them can be accommodated in a single die, thus increasing chip computational capabilities. However, transistors cannot get much smaller than their current size. The quantum-dot cellular automata (QCA) approach represents one of the possible solutions in overcoming this physical limit, even though the design of logic modules in QCA is not always straightforward. In this brief, we propose a new adder that outperforms all state-of-the-art competitors and achieves the best area-delay tradeoff. The above advantages are obtained by using an overall area similar to the cheaper designs known in literature. The 64-bit version of the novel adder spans over 18.72 μ2 of active area and shows a delay of only nine clock cycles, that is just 36 clock phases.

59 citations


Cites background or methods from "New Decomposition Theorems on Major..."

  • ...By applying the decomposition method demonstrated in [16], the computational paths of the CLA and the CFA are reduced to 7 + To introduce the novel architecture proposed for implementing ripple adders in QCA, let consider two n-bit addends A = a n−1 , . . . , a 0 and B = b n−1 , . . . , b 0 and…...

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  • ...Moreover, similar to [16], layout partitioning can be used to make the ILP-based method applicable for large layouts....

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  • ...Special efforts are directed to arithmetic circuits [2]–[16], with the main interest focused on the binary addition [11]–[16] that is the basic operation of any digital system....

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  • ...It achieved speed performances higher than all the existing QCA adders, with an area requirement comparable with the cheap RCA and CFA demonstrated in [13] and [16]....

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References
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Journal ArticleDOI
TL;DR: In this article, the authors proposed a new paradigm for computing with cellular automata (CAS) composed of arrays of quantum devices, which is called edge driven computing (EDC), where input, output and power are delivered at the edge of the CA array only; no direct flow of information or energy to internal cells is required.
Abstract: The authors formulate a new paradigm for computing with cellular automata (CAS) composed of arrays of quantum devices-quantum cellular automata. Computing in such a paradigm is edge driven. Input, output, and power are delivered at the edge of the CA array only; no direct flow of information or energy to internal cells is required. Computing in this paradigm is also computing with the ground state. The architecture is so designed that the ground-state configuration of the array, subject to boundary conditions determined by the input, yields the computational result. The authors propose a specific realization of these ideas using two-electron cells composed of quantum dots. The charge density in the cell is very highly polarized (aligned) along one of the two cell axes, suggestive of a two-state CA. The polarization of one cell induces a polarization in a neighboring cell through the Coulomb interaction in a very non-linear fashion. Quantum cellular automata can perform useful computing. The authors show that AND gates, OR gates, and inverters can be constructed and interconnected.

1,540 citations

Journal ArticleDOI
TL;DR: This work examines the possible implementation of logic devices using coupled quantum dot cells, which use these cells to design inverters, programmable logic gates, dedicated AND and OR gates, and non‐interfering wire crossings.
Abstract: We examine the possible implementation of logic devices using coupled quantum dot cells. Each quantum cell contains two electrons which interact Coulombically with neighboring cells. The charge distribution in each cell tends to align along one of two perpendicular axes, which allows the encoding of binary information using the state of the cell. The state of each cell is affected in a very nonlinear way by the states of its neighbors. A line of these cells can be used to transmit binary information. We use these cells to design inverters, programmable logic gates, dedicated AND and OR gates, and non‐interfering wire crossings. Complex arrays are simulated which implement the exclusive‐OR function and a single‐bit full adder.

1,149 citations


"New Decomposition Theorems on Major..." refers methods in this paper

  • ...The QCA paradigm is based on a cell with four quantum dots [1], [11], [12]....

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  • ...Single-bit adder designs are reported in [1]–[3]....

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Journal ArticleDOI
TL;DR: This paper describes a project to create a novel design and simulation tool for quantum-dot cellular automata (QCA), namely QCADesigner, which has already been used to design full-adders, barrel shifters, random-access memories, etc.
Abstract: This paper describes a project to create a novel design and simulation tool for quantum-dot cellular automata (QCA), namely QCADesigner. QCA logic and circuit designers require a rapid and accurate simulation and design layout tool to determine the functionality of QCA circuits. QCADesigner gives the designer the ability to quickly layout a QCA design by providing an extensive set of CAD tools. As well, several simulation engines facilitate rapid and accurate simulation. This tool has already been used to design full-adders, barrel shifters, random-access memories, etc. These verified layouts provide motivation to continue efforts toward a final implementation of QCA circuits.

827 citations


"New Decomposition Theorems on Major..." refers background or result in this paper

  • ...5 shows the layout in QCADesigner [10] for 8-bit CLA....

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  • ...[10] K. Walus, T. Dysart, G. Jullien, and R. Budiman, “QCADesigner: A rapid design and simulation tool for quantum-dot cellular automata,” IEEE Trans....

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  • ...We also give detailed results of simulations of various adders in QCADesigner [10]....

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Journal ArticleDOI
TL;DR: A method for reducing the number of majority gates required for computing three-variable Boolean functions is developed to facilitate the conversion of sum-of-products expression into QCA majority logic.
Abstract: The basic Boolean primitive in quantum cellular automata (QCA) is the majority gate. In this paper, a method for reducing the number of majority gates required for computing three-variable Boolean functions is developed to facilitate the conversion of sum-of-products expression into QCA majority logic. Thirteen standard functions are introduced to represent all three-variable Boolean functions and the simplified majority expressions corresponding to these standard functions are presented. We describe a novel method for using these standard functions to convert the sum-of-products expression to majority logic. By applying this method, the hardware requirements for a QCA design can be reduced. As an example, a 1-bit QCA adder is constructed with only three majority gates and two inverters. The adder is designed and simulated using QCADesigner, a design and simulation tool for QCA. We will show that the proposed method is very efficient and fast in deriving the simplified majority expressions in QCA design.

377 citations


"New Decomposition Theorems on Major..." refers background in this paper

  • ...The motivation for the works in [6] and [7] is the research on minimal realizations for three-variable functions described in [8]....

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Posted Content
TL;DR: This work considers an approach to definition of a scheme with "history", valid for quantization both irreversible and reversible classical CA directly using local transition rules, using language of vectors in Hilbert spaces instead of C*-algebras.
Abstract: In recent work [quant-ph/0405174] by Schumacher and Werner was discussed an abstract algebraic approach to a model of reversible quantum cellular automata (CA) on a lattice. It was used special model of CA based on partitioning scheme and so there is a question about quantum CA derived from more general, standard model of classical CA. In present work is considered an approach to definition of a scheme with "history", valid for quantization both irreversible and reversible classical CA directly using local transition rules. It is used language of vectors in Hilbert spaces instead of C*-algebras, but results may be compared in some cases. Finally, the quantum lattice gases, quantum walk and "bots" are also discussed briefly.

348 citations


"New Decomposition Theorems on Major..." refers methods in this paper

  • ...The QCA paradigm is based on a cell with four quantum dots [1], [11], [12]....

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