Research Article  Open Access
Amir Mokhtar Chabi, Samira Sayedsalehi, Shaahin Angizi, Keivan Navi, "Efficient QCA Exclusiveor and Multiplexer Circuits Based on a NanoelectronicCompatible Designing Approach", International Scholarly Research Notices, vol. 2014, Article ID 463967, 9 pages, 2014. https://doi.org/10.1155/2014/463967
Efficient QCA Exclusiveor and Multiplexer Circuits Based on a NanoelectronicCompatible Designing Approach
Abstract
Quantumdot cellular automata (QCA) are a transistorless computation approach which encodes binary information via configuration of charges among quantum dots. The fundamental QCA logic primitives are majority and inverter gates which can be utilized to design various QCA circuits. This study presents a novel approach to designing efficient QCAbased circuits based on Boolean expressions achieved from reconfiguration of fiveinput and threeinput majority gates. Whereas the multiplexer and Exclusiveor are the most important fundamental logical circuits in digital systems, designing efficient and single layer structures without coplanar crossover wiring is advantageous in QCA technology. In order to demonstrate the efficiency and usefulness of the proposed approach, simple and dense multiplexer and Exclusiveor structures are implemented. The proposed designs have significant improvement in terms of area, complexity, latency, and gate count in comparison to previous designs. The correct logical functionalities of presented structures have been authenticated using QCA designer tool.
1. Introduction
Due to current serious exiting challenges in conventional transistor technology, researchers are searching to find an alternative to this technology. Among these new technologies, quantumdot cellular automata (QCA) are a suitable alternative that offers unique features such as small feature size and ultralow power consumption and can operate at THz frequencies and room temperature [1, 2].
The basic elements in QCA are cells; each cell is composed of two mobile electrons that are located in opposite corners according to columbic energy, resulting in two possible polarizations (, ) as shown in Figure 1(a) [3].
(a)
(b)
(c)
(d)
Up to this time, many methods for fabrication of QCA basic cells are suggested such as metal island [4], magnetic [5], semiconductor [6], and molecular QCA [7]. As is discussed in [8], metal dot implementations have proven to be the most successful material systems which are based on singleelectron transistors’ fabrication techniques. The magnetic implementation is firstly proposed by Cowburn’s group and extended by the Porod group and the Bokar group. In the semiconductor physical implementation, the Cavendish group of Smith et al. proved QCA operation in GaAs/AlGaAs heterostructures with confining topgate electrodes and the group of Kern et al. demonstrated a silicon QCA cell by employing an etching technique to form the dots. Furthermore, based on [8], the Fehlner and Lapinte groups have performed successful molecular synthesis in creating molecules that show the essential bistability.
According to the columbic interaction between electrons in neighboring cells, the basic logic gates in QCA circuits (inverter and majority gates) are constructed as shown in Figures 1(b) and 1(c), respectively [9–11]. The logical functions of threeinput majority gate and fiveinput majority gate [9] (Figure 1(d)) are
This paper presents a new method to design wellorganized QCA circuits that reduces the hardware requirements when compared to previously reported circuits. Multiplexer and Exclusiveor are the most significant components in logical systems, so these circuits are optimized based on this method.
The remainder of this paper is arranged as follows. In Section 2, a review on stateoftheart designs is provided. Section 3 introduces the new approach to implementing QCAbased structures and proposes efficient and feasible designs for multiplexer and Exclusiveor. In Section 4, we use simulation results obtained from QCADesigner tool to prove the functional correctness of our proposed designs and finally Section 5 concludes the paper.
2. StateoftheArt
As mentioned earlier, the main purpose of this paper is to design two main structures for implementation of various logic circuits, so in this section previous designs are reviewed in order of 2to1 multiplexer and Exclusiveor.
2.1. Multiplexer
Multiplexers have a considerable role in the digital systems which allow us to select one of the input’s flows for transmitting to the output. Whereas all the logic functions can be built by multiplexers, implementation of multiinput multiplexer in one layer is a remarkable subject. In conventional implementation of multiplexer, there are several structures that have been introduced in [12–22]; all these designs have tried to present improved structure rather than the other. These designs have been implemented using three threeinput majority gates in different ways with different propagation delay and consumed cells according to the form of majority gate’s concatenation. One of the best proposed structures in terms of complexity and latency is introduced in [17], as shown in Figure 2(a). An innovative methodology for designing 2to1 multiplexer is introduced in [16]. This design has a modular structure that consists of several elementary blocks as illustrated in Figure 2(b). It is noteworthy that the latency of the circuits in large scales has been diminished by utilizing the presented methodology.
(a)
(b)
These designs have been implemented according to the following equation:
2.2. Exclusiveor
Due to the momentous usage of Exclusiveor component in various tasks such as parity checking and detection and correction mechanism in the receiver and sender units, designing an efficient and high speed Exclusiveor is one of the most important challenges in QCA studies. According to the position of the input signals in the Exclusiveor structure, most of the presented designs are implemented based on the multilayer or coplanar crossover wiring. In [23, 24], useful implementations of XOR gate are presented which use coplanar crossover wiring, as demonstrated in Figure 3. These designs have a similar 1.5 clock cycle delay for transmitting input signals to the output.
(a)
(b)
3. Proposed Designing Approach
The main building block of QCA circuits is majority gate and consequently the other logic circuits are implemented based on majority gate networks. In this section, we are going to propose a novel designing approach to implementing QCA logic circuits with least hardware overhead. To overcome this goal, in addition to threeinput majority gate, we have employed the fiveinput majority gate. In this approach, some functional logic circuits are implemented by configuration of fiveinput majority gate inputs.
As shown in Figure 4, , , and are labeled as the main inputs and the control input is labeled as control line. In addition, one of these inputs has twice the effect of the other inputs on fiveinput majority gate. By setting control line to “1” logic value, the Boolean function is obtained. Furthermore, logical function can be achieved by changing the value of the control line to “0.”
By using the fiveinput majority function (2), we get the following equations: It is worth mentioning that these functions need only one fiveinput majority gate for implementation. However, these functions are designed with two threeinput majority gates in the conventional method.
From the achieved equations, we can conclude that most of the combinational and sequential circuits can be constructed by assigning proper functions or fixed values to their parameters. The next section provides implementation steps of multiplexer and Exclusiveor circuits based on this method.
3.1. Multiplexer Design
As noted above, a feasible design for 2to1 multiplexer can be obtained by utilizing the proposed novel method. According to the 2to1 multiplexer function, the inputs of logical function should be changed as in Figure 5(a).
(a)
(b)
The logic function should be fed to input and also the inputs and should be fed to the inputs and , respectively. For implementation of logical function , a threeinput majority gate has been used. It is to be noted that only two majority gates and one inverter gate are used for implementing this structure.
By applying this method, the equation of 2to1 multiplexer is defined as follows: To clarify the correct functionality of the proposed design in detail, the truth table of proposed circuit is shown in Table 1 with three output columns. The first column presents eight possible combinations of three input cells (, , and ). The second column demonstrates the output of threeinput majority gate which produces the logical function . The summation of fiveinput majority gate inputs is shown in the third column and the last column illustrates the main output of the proposed 2to1 multiplexer circuit.

As it is obvious in Figure 5(b), the latency of proposed multiplexer is 0.75 clock cycle, so this design is the fastest in comparison to previous mentioned designs.
3.2. Exclusiveor Design
In this section, we propose our new high speed and single layer twoinput XOR gate using the equation mentioned above. The applied equation which is achieved using the majority gate functions is shown in (9). As illustrated in Figure 6(a), the output of threeinput majority gate () with twice the effect and inverse of signal and signal are assigned to the fiveinput majority gate in the similar clocking zone. Consequently, the Exclusiveor of and signals is produced in the next clocking zone. Considering the similar procedure, we get the equation of twoinput XOR gate as follows: The propagation delay of the presented twoinput XOR gate is 0.75 clock cycle with huge reduction in cell counts and area occupation. The significant contribution of this design is implemented in signal layer without using rotated cells in comparison to previous designs. This structure can be expanded to the larger scale by cascading several twoinput XOR gates. As example, the schematic of fourinput XOR gate and its QCA implementation are shown in Figure 7.
(a)
(b)
(a)
(b)
4. Simulation Results
QCADesigner is a wellknown simulation tool generally expanded for evaluating QCA logic circuits; this tool has two different simulation engines which are called bistable approximation and coherence vector. The bistable approximation engine calculates state of a single cell using a timeindependent approach with kink energy formula that calculates cost of two cells having opposite polarizations, so simulation time in this engine is reduced. The coherence vector model considers the timedependent state of a cell in interaction with the other cells through the same kink energy formula [25–27].
In QCADesigner software, each single cell (standard, rotated) can act in four modes (input, output, fixed, and normal) which is shown in Figure 8.
(a)
(b)
(c)
(d)
In this section, correct functionality of the proposed structures is authenticated using QCADesigner tool version 2.0.3 [25]. Each one of the circuits is examined under both simulation engines (bistable approximation and coherence vector) and similar outcomes are achieved. Tables 2 and 3 illustrate the applied parameters in bistable approximation and coherence vector simulation engines, respectively.


The analysis of output waveforms verifies the accuracy and efficiency of presented designs in comparison to stateoftheart designs. The simulation results of proposed 2to1 multiplexer and 4to1 multiplexer are illustrated in Figures 9(a) and 9(b), respectively. As is clear in Figure 9(a), the first meaningful output appears in 0.75 clock cycle.
(a)
(b)
In Figures 10(a) and 10(b), simulation results of twoinput and fourinput Exclusiveor circuits are authenticated. Latency of the twoinput and fourinput XOR gates is 0.75 and 2.75 clock cycle, respectively.
(a)
(b)
Table 4 comprises the previous works in 2to1 and 4to1 multiplexer’s designs with the proposed multiplexers in terms of hardware requirement and latency.

According to Table 5, it can be concluded that this proposed design results in significant improvements in gate count, area, cell count, and latency. The comparison results of Exclusiveor circuits are illustrated in Table 6. Based on the obtained results, it can be concluded that employing the proposed approach in QCA circuits leads to a considerable optimization in cell count, occupation area, and propagation delay.

5. Conclusion
In this paper, the new approach to implementation of QCAbased circuit was introduced. This method is based on the new configuration of fiveinput majority gate that led to achieve significant Boolean function such as . It is expected that the novel method presented in this paper will produce efficient QCAbased logical circuits such as multiplexer and Exclusiveor. These proposed circuits surpass previous designs in terms of gate count, area, cell count, and latency. Furthermore, the great advantage of the presented approach is that it leads to implementation of these structures in single layer without any crossover wiring.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
References
 J. M. Seminario, P. A. Derosa, L. E. Cordova, and B. H. Bozard, “A molecular device operating at terahertz frequencies: theoretical simulations,” IEEE Transactions on Nanotechnology, vol. 3, no. 1, pp. 215–218, 2004. View at: Publisher Site  Google Scholar
 R. P. Cowburn and M. E. Welland, “Room temperature magnetic quantum cellular automata,” Science, vol. 287, no. 5457, pp. 1466–1468, 2000. View at: Publisher Site  Google Scholar
 C. S. Lent, P. D. Tougaw, W. Porod, and G. H. Bernstein, “Quantum cellular automata,” Nanotechnology, vol. 4, no. 1, pp. 49–57, 1993. View at: Publisher Site  Google Scholar
 G. Tóth and C. S. Lent, “Quasiadiabatic switching for metalisland quantumdot cellular automata,” Journal of Applied Physics, vol. 85, no. 5, pp. 2977–2984, 1999. View at: Publisher Site  Google Scholar
 G. H. Bernstein, A. Imre, V. Metlushko et al., “Magnetic QCA systems,” Microelectronics Journal, vol. 36, no. 7, pp. 619–624, 2005. View at: Publisher Site  Google Scholar
 G. L. Snider, A. O. Orlov, I. Amlani et al., “Experimental demonstration of quantumdot cellular automata,” Semiconductor Science and Technology, vol. 13, no. 8, pp. A130–A134, 1998. View at: Publisher Site  Google Scholar
 P. D. Tougaw, Quantum cellular automata: computing with quantum dot molecules [Ph.D. thesis], University of Notre Dame, 1996.
 N. G. Anderson and S. Bhanja, FieldCoupled Nanocomputing Paradigms, Progress, and Perspectives, Springer, Heidelberg, Germany. View at: Publisher Site
 K. Navi, R. Farazkish, S. Sayedsalehi, and M. Rahimi Azghadi, “A new quantumdot cellular automata fulladder,” Microelectronics Journal, vol. 41, no. 12, pp. 820–826, 2010. View at: Publisher Site  Google Scholar
 P. D. Tougaw and C. S. Lent, “Logical devices implemented using quantum cellular automata,” Journal of Applied Physics, vol. 75, no. 3, pp. 1818–1825, 1994. View at: Publisher Site  Google Scholar
 K. Navi, S. Sayedsalehi, R. Farazkish, and M. R. Azghadi, “Fiveinput majority gate, a new device for quantumdot cellular automata,” Journal of Computational and Theoretical Nanoscience, vol. 7, no. 8, pp. 1546–1553, 2010. View at: Publisher Site  Google Scholar
 K. Kim, K. Wu, and R. Karri, “The robust QCA adder designs using composable QCA building blocks,” IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems, vol. 26, no. 1, pp. 176–183, 2007. View at: Publisher Site  Google Scholar
 S. Hashemi, M. R. Azghadi, and A. Zakerolhosseini, “A novel QCA multiplexer design,” in Proceedings of the International Symposium on Telecommunications (IST '08), pp. 692–696, August 2008. View at: Publisher Site  Google Scholar
 H. Balijepalli and M. Niamat, “Design of a nanoscale quantumdot cellular automata configurable logic block for FPGAs,” in Proceedings of the 2012 IEEE 55th International Midwest Symposium on Circuits and Systems (MWSCAS '12), pp. 622–625, August 2012. View at: Publisher Site  Google Scholar
 M. Kianpour and R. SabbaghiNadooshan, “A conventional design for CLB implementation of a FPGA in Quantumdot Cellular Automata (QCA),” in Proceedings of the IEEE/ACM International Symposium on Nanoscale Architectures (NANOARCH '12), pp. 36–42, Amsterdam, Netherlands, July 2012. View at: Google Scholar
 V. A. Mardiris and I. G. Karafyllidis, “Design and simulation of modular 2^{n} to 1 quantumdot cellular automata (QCA) multiplexers,” International Journal of Circuit Theory and Applications, vol. 38, no. 8, pp. 771–785, 2010. View at: Publisher Site  Google Scholar
 S. Hashemi and K. Navi, “New robust QCA D flip flop and memory structures,” Microelectronics Journal, vol. 43, no. 12, pp. 929–940, 2012. View at: Publisher Site  Google Scholar
 D. Mukhopadhyay and P. Dutta, “Quantum cellular automata based novel unit 2:1 multiplexer,” International Journal of Computer Applications, vol. 43, no. 2, pp. 22–25, 2012. View at: Publisher Site  Google Scholar
 V. C. Teja, S. Polisetti, and S. Kasavajjala, “QCA based multiplexing of 16 arithmetic & logical subsystemsa paradigm for nano computing,” in Proceedings of the 3rd IEEE International Conference on Nano/Micro Engineered and Molecular Systems (NEMS '08), pp. 758–763, Sanya, China, January 2008. View at: Publisher Site  Google Scholar
 M. Askari, M. Taghizadeh, and K. Fardad, “Digital design using quantumdot cellular automata (A nanotechnology method),” in Proceedings of the International Conference on Computer and Communication Engineering (ICCCE '08), pp. 952–955, May 2008. View at: Publisher Site  Google Scholar
 A. M. Chabi, S. Sayedsalehi, and K. Navi, “New modules for quantumdot cellular automata AND & OR gates,” Canadian Journal on Electrical and Electronics Engineering, vol. 3, no. 5, pp. 200–208, 2012. View at: Google Scholar
 A. Sarkar and D. Mukhopadhyay, “Improved quantum dot cellular automata 4 : 1 multiplexer circuit unit,” SOP Transactions on NanoTechnology, vol. 1, no. 1, pp. 37–44, 2014. View at: Google Scholar
 M. T. Niemier, Designing digital systems in quantum cellular automata [M.S. thesis], University of Notre Dame, 2004.
 S. Hashemi, R. Farazkish, and K. Navi, “New quantum dot cellular automata cell arrangements,” Journal of Computational and Theoretical Nanoscience, vol. 10, no. 4, pp. 798–809, 2013. View at: Publisher Site  Google Scholar
 QCADesigner Documentation, http://www.qcadesigner.ca/.
 K. Kim, K. Wu, and R. Karri, “Quantumdot Cellular Automata design guideline,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. E89A, no. 6, pp. 1607–1614, 2006. View at: Publisher Site  Google Scholar
 K. Walus, T. J. Dysart, G. A. Jullien, and R. A. Budiman, “QCADesigner: a rapid design and simulation tool for quantumdot cellular automata,” IEEE Transactions on Nanotechnology, vol. 3, no. 1, pp. 26–31, 2004. View at: Publisher Site  Google Scholar
Copyright
Copyright © 2014 Amir Mokhtar Chabi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.