# Two Novel Quantum-Dot Cellular Automata Full Adders

Authors: Mahdie Qanbari; Reza Sabbaghi-Nadooshan
Journal: Journal of Engineering
 (2013)

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## Abstract

Quantum-dot cellular automata (QCA) is an efficient technology to create computing devices. QCA is a suitable candidate for the next generation of digital systems. Full adders are the main member of computational systems because other operations can be implemented by adders. In this paper, two QCA full adders are introduced. The first one is implemented in one layer, and the second one is implemented in three layers. Five-input majority gate is used in both of them. These full adders are better than pervious designs in terms of area, delay, and complexity.


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## Body

## 1. Introduction

Quantum-dot cellular automata (QCA) is a new nanotechnology that can help us to reach low-power consumption, high device density, and high clock frequency. QCA size is smaller than CMOS it can, even be implemented in molecule or atom size. QCA power consumption is extremely lower than CMOS because there are not any current in the circuit and output capacity. The two important gates in QCA are three-input majority gate and inverter. In this paper, two novel QCA full adders are introduced in which the first one is implemented in one layer and the second one is implemented in three layers. They have five-input majority gate in their structure.The rest of the paper is as follows. Section2 describes QCA. Section 3 describes five-input majority gates. Two new full adders are presented in Section 4. Finally, Section 5 concludes the paper.


## 2. Quantum-Dot Cellular Automata (QCA)

Quantum-dot cellular automata (QCA), first proposed in 1993 by Lent et al. [1], is a structure made up of identical cells realized through a variety of technologies such as electrodynamic, ferromagnetic, and molecular [2].A QCA cell a square shape, with four quantum dots in which just two electrons can stand at it. The electrons perch diagonally in the square for getting the farthest position from each other because of coulombic repulsive force. When the two electrons are positioned as in Figure1(a), the polarization is (+1), and if they are positioned as  in Figure 1(b), the polarization is (−1).The polarization of cells.
(a)
(b)A QCA wire can be built by placing a row of cells as shown in Figure2 when the first cell’s polarization is +1, the other’s polarization becomes +1, and when the input cell’s polarization is −1, the other cell’s polarization has the same value.Figure 2
A QCA wire.The most important gates in QCA are inverters and three-input majority gates. The inverter is shown in Figure3(a), when the input cell has a value, the output cell become reversed. A three-input majority gate is made of three inputs, one device cell and one output as shown in Figure 3(b). If most of inputs have polarization +1, the device cell becomes +1. If most of inputs have polarization −1, the device cell becomes −1. The output cell’s polarization follows the device cell’s polarization.(a) A QCA inverter. (b) A QCA majority gate.
(a)
(b)AND gates and OR gates can be implemented by three-input majority gate. If one of the inputs be +1, then the three-input majority gate is like an OR gate (1). If one of the inputs be −1, then the three-input majority gate is like an AND gate (2):
(1)Maj(A,B,1)=A+B,(2)Maj(A,B,0)=A·B.
A QCA clocking zone is a group of QCA cells which is controlled by the same QCA clock. In QCA, four clocking zones are considered. The schematic of a QCA wire constructed using four clocking zones is shown in Figure 4(a). There is a 90° phase delay from one clocking zone to the next one as shown in Figure 4(b) [6].(a) A QCA wire with four clocking zones, (b) QCA clocks wave forms.
(a)
(b)


## 3. Five-Input Majority Gates

For reaching our goal, we need another gate and it is called five-input majority gates.There are many five-input majority gates which were proposed from 2007 until now. As shown in Figure5, Azghadi et al. [3], Navi et al. [4, 5], Akeela and Wagh [2], and Hashemi et al. [6] introduced some five-input majority gates. These five-input majority gates have some advantages and disadvantages.The proposed five-input majority gates in the literature ((a) [3], (b) [4], (c) [5], (d) [2], (e) [6], (f) [6]).
(a)
(b)
(c)
(d)
(e)
(f)We examined and found that the five-input majority gate, which was proposed in [2], is the best choice for our full adder, because it has ordinary cells, the inputs and outputs are not surrounded by the other cells, and they can be accessed easily. This design is suitable to implement larger QCA circuits, so we choose it for our full adder.


## 4. Two Novel QCA Full Adders

Many QCA full adders have been introduced until now. The first one is presented by Tougaw and Lent in 1994 [7]. As it is shown in Figure 6, it has five three-input majority gates and three inverters. This full adder uses QCA coplanar wire crossing scheme [6]. It is implemented in one layer, and it has 192 cells. In this design, QCA clocking concepts are not considered [6]. Another QCA full adders using some logical structures is introduced by Vetteth et al. in 2002 [9], but the QCA clocking concepts are considered at it. For generating the output, it takes 3/5 clock cycles. Another QCA full adder is introduced by  Wang et al. in 2003 [8], which is made of three three-input majority gates and two inverters. It takes 1/25 clock cycles to produce outputs. The schematic of this full adder is shown in Figure 7.Figure 6
One-bit QCA full adder schematic [7].Figure 7
One-bit QCA full adder schematic [8].There are some QCA full adders that are implemented in three layers by Cho [10], Cho and Swartzlander [11, 12], Hänninen and Takala [13], Kim et al. [14], Zhang et al. [15], Navi et al. [4, 5], Sayedsalehi et al. [16], and Hashemi et al. [6].In this paper, we proposed two QCA full adders in which the first one is implemented in one layer and the second one is implemented in three layers. In these designs, at first the carry value is calculated by a three-input majority gate (3), and then the carry value is inverted and is used as the two inputs of the five-input majority gate. The output of the five-input majority gate generates the some value:
(3)Carry=Maj3(A0,B0,C0),(4)Sum=Maj5(A0,B0,C0,Carry′,Carry′).In this paper, two full adders were simulated by QCA designer software (version 2.0.3) [17]. The coherence vector computational engine was used in all simulations, and the important parameters are cell size = 18 nm  ×  18 nm, dot diameter = 5 nm, and radius of effect = 40 nm.The first full adder uses QCA coplanar wire crossing scheme. As shown in Figure8, this full adder takes one clock cycles to generate output. It has 104 QCA cells, and its area is 0.13 μm2. The simulation result has been shown in Figure 9.Figure 8
The first QCA full adder (it is implemented in one layer).Figure 9
The simulation results of the first QCA full adder.The second full adder is implemented in three layers. This full adder takes 0.75 clock cycles to generate output as shown in Figure10. It has 63 QCA cells and its area is 0.05 μm2. In this full adder like the previous full adder, the inputs and outputs are not surrounded by the other cells and they can be accessed easily; the sum value and the carry out value come out from the same side, and they are suitable to implement larger QCA circuits. The simulation result has been shown in Figure 11.Figure 10
The second QCA full adder (it is implemented in three layers).Figure 11
The simulation results of the second QCA full adder.Table1 compares our designs and the best previous designs. The first full adder is better than the previous designs which were implemented in one layer in terms of area, delay, and complexity. Also, the second one is better than the previous designs which were implemented in three layers in terms of delay and complexity.Table 1
The comparison between our proposed designs and the best previous designs.
QCA full adders
Layer’s number
Complexity (cells)
Area (μm2)
Latency (clk cycle)
Coplanar QCA FA [8]
1
145
0.17
1.25
Proposed QCA FA in Figure8
1
104
0.13
1
Multilayer QCA FA [6]
3
79
0.05
1.25
Proposed QCA FA in Figure10
3
63
0.05
0.75


## 5. Conclusions

As mentioned earlier, low power consumption, high device density, and high clock frequency are the goal of QCA technology.In this paper, two novel QCA full adders were proposed in which the first one is implemented in one layer and the second one is implemented in three layers. They have ordinary cells, and the inputs and outputs are not surrounded by the other cells and they can be accessed easily. The sum value and the carry out value come out from the same side and they are suitable to implement larger QCA circuits. The first full adder is better than the previous designs in terms of area, delay, and complexity. The second full adder is better than the previous designs in terms of delay and complexity but its area and the best previous designs area are equal.



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*Source: 561651-2013-05-19.xml*