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Design and implementation of an efficient single layer five input majority voter gate in quantumdot cellular automata
SpringerPlus volume 5, Article number: 636 (2016)
Abstract
The fundamental logical element of a quantumdot cellular automata (QCA) circuit is majority voter gate (MV). The efficiency of a QCA circuit is depends on the efficiency of the MV. This paper presents an efficient single layer fiveinput majority voter gate (MV_{5}). The structure of proposed MV_{5} is very simple and easy to implement in any logical circuit. This proposed MV_{5} reduce number of cells and use conventional QCA cells. However, using MV_{5} a multilayer 1bit fulladder (FA) is designed. The functional accuracy of the proposed MV_{5} and FA are confirmed by QCADesigner a wellknown QCA layout design and verification tools. Furthermore, the power dissipation of proposed circuits are estimated, which shows that those circuits dissipate extremely small amount of energy and suitable for reversible computing. The simulation outcomes demonstrate the superiority of the proposed circuit.
Background
Now a day’s, CMOS technology is approaching its physical boundary and facing earnest challenges by designing perpetually incrementing frequencies and downscaling of computational devices. This technology has found many complication like high leakage current, high power consumption, high lithography cost, low density problem and limitation of speed in GHz range. Therefore, to overcome the deficiencies an extensive research on nanotechnologies must be taken into consideration. A report of ITRS (International Technology Road 2013) shows a road map of future computing technologies. Quantumdot cellular automata (Lent et al. 1993; Orlov et al. 1997) is one of the promising alternative technologies that proffers an innovative approach and has exhibited ultra low power, extreme speed and highly dense digital devise designing capabilities. In addition, QCA based memory unit, reversible logic and arithmetic logic circuit have been considered in several studies (Kim et al. 2007; Navi et al. 2010; Hänninen and Takala 2010; Hashemi et al. 2012; Qanbari and SabbaghiNadooshan 2013; Kianpour and SabbaghiNadooshan 2014; Sayedsalehi et al. 2015; Angizi et al. 2015; Bahar et al. 2015).
The rudimentary element of QCA circuit is a majority gate (MV); digital operation can be employed by using MV. MV characterizes and determines the function value based on majority verdict (Oya et al. 2003). Up to now, most QCA circuits have been investigated and designed only by means of 3input majority gates (MV_{3}). However, if these circuits are constructed using 5input majority gates (MV_{5}), they would be optimized in cell counts, area and complexity.
To reveal the effectiveness of proposed MV_{5}, a QCA fulladder has been designed using proposed MV_{5}. Results reveal the superiority of proposed FA in terms of latency, cell counts and area to other previous designs (Tougaw and Lent 1994; Wang et al. 2003; Zhang et al. 2004; Azghadi et al. 2007; Cho and Swartzlander 2007, 2009).
Proposed fiveinput majority gate
MV_{5} is a cell arrangement which includes five input cells, one output and some device cells. The logic function of MV_{5} can be presented as Eq. (1), where the inputs are labeled as A, B, C, D and E respectively. The truth table of the MV_{5} is shown in Table 1.
The proposed design of MV_{5} is shown in Fig. 1. In this design, A, B, C, D and E are labeled as inputs and the output cell is labeled as OUTPUT. Additionally, three middle cells are labeled 1, 2 and 3. Polarization of input cells are fixed and middle cells and output cell are free to change. Here, cell “A” has an impact on all the middle cells. Similarly, cell “B”, cell “C” cell “D” and cell “E” also have an impact on all the middle cells. These impacts are propagated to the output cell and construct the MV_{5} output, efficiently. The propose MV_{5} requires only nine cells and uses conventional QCA cells to implement.
Physical proofs
To carry out the physical proofs, the below postulates are considered:

All cells are alike and the distance of end to end of each cell is 18 nm.

The space between two neighbor cells is 2 nm shown in Fig. 2.
The proposed MV_{5} has approximately 32 distinct input states; we should verify all the input condition to validate the accuracy of the gate. In this paper, only one state (A = 1, B = 0, C = D = E = 1) has been considered for verification. Similarly, other states can be verified too. For a fixed input MV_{5}, the five input cells polarization are remain unchanged; only the intermediary cells and the output cell are subject to be changed to their polarization according to the input cells. Here, the proposed MV_{5} have three intermediary cells and one output cell those are labeled as 1, 2, 3 and OUTPUT respectively shown in Fig. 1.
A structure is said to be stable, when the QCA cells are assembled with their minimum potential energies. The potential energy between two different cell electrons can be computed using the Eq. (2) (Halliday and Resnick 2004; McDermott 1984; Halloun and Hestenes 1985). Here, U is potential energy; a fixed colon is k, q _{1} and q _{2} are electric charges, and the distance between two electric charges is r. The total potential energy of a given structure is “U _{ T }” and that can be calculated using Eq. (3).
For, finding the stable structure, one needs to calculate the potential energy U _{ i } for each middle cell. Here, cell 1 has two different polarization state; polarization P = +1 and P = −1 shown in Fig. 3.
Now, considering state 3 (a); here the potential energy for cell 1 U _{ T } is the summation of potential energies of both x and y electrons. Potential energy for x and y electrons are the total energy exist between each electron (e _{1}, e _{2}, e _{3}, e _{4}, e _{5}, e _{6}, e _{7}, e _{ 8 }, e _{ 9 }, and e _{10}) with electron x and y respectively, which is calculated using Eq. (2). Finally, using Eq. (3) total potential energy for “cell 1” can be calculated. Similarly, potential energy of “cell 1” for state 3.3 (b) can be calculated. The necessary calculations for finding the total potential energies of structure (a) and structure (b) are given below:
Figure 3a (For electron x)  Figure 3a (For electron y) 

\(U_{1} = \frac{A}{{r_{1} }} = \frac{{23.04 \times 10^{  29} }}{{20 \times 10^{  9} }} \approx 1.15 \times 10^{  20} J\) \(U_{2} = \frac{A}{{r_{2} }} = \frac{{23.04 \times 10^{  29} }}{{18.11 \times 10^{  9} }} \approx 1.27 \times 10^{  20} J\) \(U_{3} = \frac{A}{{r_{3} }} = \frac{{23.04 \times 10^{  29} }}{{2 \times 10^{  9} }} \approx 11.52 \times 10^{  20} J\) \(U_{4} = \frac{A}{{r_{4} }} = \frac{{23.04 \times 10^{  29} }}{{26.91 \times 10^{  9} }} \approx 0.86 \times 10^{  20} J\) \(U_{5} = \frac{A}{{r_{5} }} = \frac{{23.04 \times 10^{  29} }}{{20 \times 10^{  9} }} \approx 1.15 \times 10^{  20} J\) \(U_{6} = \frac{A}{{r_{6} }} = \frac{{23.04 \times 10^{  29} }}{{42.04 \times 10^{  9} }} \approx 0.55 \times 10^{  20} J\) \(U_{7} = \frac{A}{{r_{7} }} = \frac{{23.04 \times 10^{  29} }}{{44.72 \times 10^{  9} }} \approx 0.52 \times 10^{  20} J\) \(U_{8} = \frac{A}{{r_{8} }} = \frac{{23.04 \times 10^{  29} }}{{43.91 \times 10^{  9} }} \approx 0.53 \times 10^{  20} J\) \(U_{9} = \frac{A}{{r_{9} }} = \frac{{23.04 \times 10^{  29} }}{{44.72 \times 10^{  9} }} \approx 0.52 \times 10^{  20} J\) \(U_{10} = \frac{A}{{r_{10} }} = \frac{{23.04 \times 10^{  29} }}{{69.34 \times 10^{  9} }} \approx 0.33 \times 10^{  20} J\) \(U_{{T_{{}} x_{1} }}^{  } = \sum\nolimits_{i = 1}^{10} {U_{i} } = 18.38 \times 10^{  20} J\)  \(U_{1} = \frac{A}{{r_{1} }} = \frac{{23.04 \times 10^{  29} }}{{42.04 \times 10^{  9} }} \approx 0.55 \times 10^{  20} J\) \(U_{2} = \frac{A}{{r_{2} }} = \frac{{23.04 \times 10^{  29} }}{{20 \times 10^{  9} }} \approx 1.15 \times 10^{  20} J\) \(U_{3} = \frac{A}{{r_{3} }} = \frac{{23.04 \times 10^{  29} }}{{26.91 \times 10^{  9} }} \approx 0.86 \times 10^{  20} J\) \(U_{4} = \frac{A}{{r_{4} }} = \frac{{23.04 \times 10^{  29} }}{{38 \times 10^{  9} }} \approx 0.61 \times 10^{  20} J\) \(U_{5} = \frac{A}{{r_{5} }} = \frac{{23.04 \times 10^{  29} }}{{18.11 \times 10^{  9} }} \approx 1.27 \times 10^{  20} J\) \(U_{6} = \frac{A}{{r_{6} }} = \frac{{23.04 \times 10^{  29} }}{{20 \times 10^{  9} }} \approx 1.15 \times 10^{  20} J\) \(U_{7} = \frac{A}{{r_{7} }} = \frac{{23.04 \times 10^{  29} }}{{58.03 \times 10^{  9} }} \approx 0.40 \times 10^{  20} J\) \(U_{8} = \frac{A}{{r_{8} }} = \frac{{23.04 \times 10^{  29} }}{{44.72 \times 10^{  9} }} \approx 0.52 \times 10^{  20} J\) \(U_{9} = \frac{A}{{r_{9} }} = \frac{{23.04 \times 10^{  29} }}{{22.09 \times 10^{  9} }} \approx 1.04 \times 10^{  20} J\) \(U_{10} = \frac{A}{{r_{10} }} = \frac{{23.04 \times 10^{  29} }}{{44.72 \times 10^{  9} }} \approx 0.52 \times 10^{  20} J\) \(U_{{T_{{y_{1} }} }}^{  } = \sum\nolimits_{i = 1}^{10} {U_{i} } = 8.05 \times 10^{  20} J\) 
Total potential energy of Fig. 3a is
Similarly, the total potential energy for Fig. 3b can be calculated and it is
With comparison of the achieved results, the electrons in cell 1 are located in state (a) is more stable because it has the lower potential energy than state (b). Similar the potential energy for cell 2 and cell 3 can be calculated and the final results are mentioned as.
Proposed QCA fulladder
The proposed MV_{5} is implemented by designing an efficient QCA fulladder. The schematic diagram of newly proposed QCA fulladder is shown in Fig. 4.
This fulladder is designed using the planar designing concept. The proposed FA has been implemented using 2inverters and 2MVs. In comparison with the earlier FA (Azghadi et al. 2007), it has an extra inverter gate. The structure of proposed MV_{5}, it would be easier to employ 2inverters rather than 1inverter and some wires for transmitting the inverted signal to other part. The proposed QCA FA is simple in structure and easy to construct. In this design, at first the carry value is calculated and then takes its inversion value and uses this value as an input of the MV_{5} gates.
Power dissipation of proposed QCA fulladder
The power dissipates from a single cell depends on the rate of change of the clock and the tunneling energy. The power dissipation of a QCA circuit in a single clock phase can be simply calculated by adding the power dissipated by each majority gate and inverter (Liu et al. 2012).
Using Hamming distance (HD) power dissipation of a QCA circuit can be estimated. Power dissipation is depends on HD between input cells to inverter cells as well as HD between majority voter gates (Liu et al. 2012). For an inverter when the input is changed from 0 → 0 or 1 → 1. In this case the HD will be 0, and the power dissipation by inverter at γ = 0.25 E _{ k } and T = 2.0 K is 0.8 meV whereas for γ = 1.0 E _{ k }, it is 8.0 meV (Liu et al. 2012). If the input is changed from 0 → 1 or 1 → 0, in this case the HD will be 1 and the power dissipation by the inverter is 28.4 meV, where T = 2.0 K and γ = 0.25 E _{ k }. For majority gate, power dissipation is minimum, when the inputs are changed from 000 → 000 i.e. HD is 0, and the power dissipation is maximum when polarization of all inputs are changed i.e. input polarization are changed from 000 → 111 i.e. HD is 3. The power dissipation by the majority voter gate for HD 0 and 3 are 0.8 and 41.0 meV respectively, where γ = 0.25 E _{ k } and T = 2.0 K (Liu et al. 2012).
By using Hamming distance based methodology described in (Liu et al. 2012), the power dissipated by the proposed MV_{5} and 1bit QCA fulladder is estimated and the results are shown in Table 2.
Simulations and results comparison
The proposed MV_{5} and FA have been simulated and verified using QCADesigner (Walus et al. 2003, 2004) only tools for QCA layout design and verification. In these simulations, both bistable and coherence vector engines have been employed to simulate. In both simulations identical outputs are obtained which confirm the correctness of the proposed designs. The simulated circuit layout and simulated output of proposed MV_{5} are shown in Fig. 5.
The proposed QCA fulladder is designed in three layers illustrated in Fig. 6. The main layer contains 34 cells, second layer contains 4 cells and the third layer contains 10 cells. Finally, it requires 48 cells and 3 clock phases to produce exact outputs (Sum and Carry).
Using QCADesigner, complexity, time delay and area consumption of QCA circuits can easily be calculated (Walus et al. 2003). Table 3 demonstrates a concise comparison between the proposed QCA FA and the earlier FA (Vetteth et al. 2002; Wang et al. 2003; Zhang et al. 2005; Cho and Swartzlander 2007; Kim et al. 2007; Cho and Swartzlander 2007, 2009; Navi et al. 2010; Hänninen and Takala 2010; Hashemi et al. 2012; Qanbari and SabbaghiNadooshan 2013) in terms of complexity, area and time delay. Here, complexity indicates the number of cell is used to design the FA. Similarly, the area represents the total covered area of the corresponding FA in micro meter. The “Latency” indicates the number of clock zone used. It also indicates the time delay of the circuit.
It is clear that the new QCA fulladder dominates all the previous designs (Vetteth et al. 2002; Wang et al. 2003; Zhang et al. 2005; Cho and Swartzlander 2007; Kim et al. 2007; Cho and Swartzlander 2007, 2009; Navi et al. 2010; Hänninen and Takala 2010; Hashemi et al. 2012; Qanbari and SabbaghiNadooshan 2013) in terms of covered area and number of cell count. It leads to a very dense structure and has the same time delay with the previous best designs (Qanbari and SabbaghiNadooshan 2013). According to the bar chat shown in Fig. 7, the proposed FA leads to around 95.17 % improvement in area and 83.6 percent improvement in cell complexity in comparison to the QCA FA designed using 3input majority gates and inverters in (Vetteth et al. 2002). This FA also, leads to around 40 % improvement in area and 23.8 % improvement in cell complexity compared to the best QCA FA designed using previous MV_{5} and inverters (Qanbari and SabbaghiNadooshan 2013).
Reliability of proposed QCA circuits
The temperature effect on the output cell’s polarization of proposed MV_{5} and QCA FA are observed. The output cell’s polarization is taken at different temperature using QCADesigner tool. The average output polarization (AOP) for each output cell is calculated from (Pudi and Sridharan 2011) and shown in Fig. 8. The proposed circuit works efficiently in temperature range of 1–6 K, and the AOP for each output cell is changed very little in this range. When the temperature is above 6 K, the AOP is dropped drastically, which results incorrect outputs.
Conclusion
A new flexible 5input majority gate and a new efficient fulladder have been presented. The proposed MV_{5} has been implemented in one layer and using nine QCA cells only. To validate the correctness and effectiveness of the proposed MV_{5} a QCA FA has been presented. Moreover the estimation of power dissipation by the proposed QCA fulladder circuits illustrates that the proposed QCA FA is highly energy efficient circuit. The proposed FA has a considerable improvement in comparison to the previous FAs in terms of covered area, number of cells and has a similar time delay to the previous best FA.
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Authors’ contributions
ANB designed the logic of proposed circuits and simulated them using QCADesigner. SW helped to calculate the power dissipation and temperature effect on AOP of proposed circuits. All authors read and approved the final manuscript.
Acknowledgements
We express our thanks to NH, Nazir Hossain, for his valuable guideline in preparing manuscript.
Competing interests
Both authors declare that they have no competing interests.
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Bahar, A.N., Waheed, S. Design and implementation of an efficient single layer five input majority voter gate in quantumdot cellular automata. SpringerPlus 5, 636 (2016). https://doi.org/10.1186/s4006401622207
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DOI: https://doi.org/10.1186/s4006401622207