Low Complexity QCA Binary to Gray Code Converter

Young-Won You1 and Jun-Cheol Jeon2

1Dept. of Computer Engineering, Kumoh Institute of Technology

61, Daehak-ro, Gumi, Gyeongbuk 730-701, Korea

yy6818@naver.com 2Corresponding Author : jcjeon@kumoh.ac.kr

Abstract. Quantum-dot cellular automata(QCA) is an emerging promising

technology that implement digital circuits. It has advantage of nanoscale and

low power consumption. Digital computers deal with binary numbers but other

code must be used to process the numbers. One of important codes, a Gray code

is important in digital communications. Variable gray code converters based on

QCA have proposed but the circuits are not considered the scalability and com-

plexity. In this paper, we propose low complexity design of binary to gray code

converter. In the circuit, an exclusive-OR(XOR) gate is important so we uses

small XOR gate using Nand-Nor-Inverter(NNI) gate. An NNI gate is universal

gate that can be used to construct all other logic gates. By using the NNI gate,

we propose two-bit binary to gray code converter. The proposed circuit is simu-

lated and compared to other circuit so that verify its performance.

Keywords: Nanotechnology, Quantum-dot Cellular Automata, Binary to Gray

Code Converter, Exclusive-OR, Nand-Nor-Inverter

1 Introduction

Scaling of CMOS devices seeks aggressive development, such as reducing transistor

size and reducing power consumption, but it has faced such limitations as current

leakage and increased power density [1]. Quantum-dot cellular automata (QCA), a

new technology that can replace this problem, is a molecular or atom-level nanoscale

device that consumes extremely low power and is attracting attention in the next gen-

eration of electronic circuit design [2]. QCA is first introduced by Lent et al. QCA has

been designed in various structures such as basic combination and sequential logic

circuits [3-7]. This paper is organized in five sections. In Section 2, a brief technical

background for QCA operation and previous research on QCA binary to gray code

converter is presented. In Section 3, the proposed circuit is presented and the proper-

ties of the proposed XOR design are discussed in Section 4. Conclusions are offered

in Section 5.

Advanced Science and Technology Letters Vol.144 (UBWCN 2017), pp.46-50

http://dx.doi.org/10.14257/astl.2017.144.06

ISSN: 2287-1233 ASTL Copyright © 2017 SERSC

2 Related Researches

2.1 QCA Basic

QCA circuit composes of quantum cells which consist of four quantum dots. Each

cell contains two electrons and the electrons switch position diagonally due to cou-

lomb repulsion. As shown in Figure 1 (a), there are two states as +1 and -1. In a sec-

ond type of QCA cells, the dots are occupied at the middle of the sides of cells as

shown in Figure 1 (b). The wires can be composed of two types of cells and it is

shown in Figure 1 (c). The three types of QCA inverter designs are shown in Figure 2.

An inverter can be constructed by locating the cells with only their corners. In the

wire, the signal is inverted because of Coulombic interaction. First inverter is used 45

degree cell and second is simple inverter. Third inverter is called robust inverter and

its information is propagated with strong signal.

Fig. 1. QCA basic concept: (a) QCA cell, (b) 45° rotated cell and (c) Two wires based 90° cell

and 45° rotated cell

Fig. 2. Three types of inverters

2.2 Previous Binary to Gray Code Converter

A binary to gray code converter consists of XOR gates. In two-bit binary to gray code

converter, it uses only one XOR gate. A block diagram of two-bit binary to gray code

+1 -1

(a)

+1 -1

(b)

Input cell(c)

Information propagation

Input cell

Output cell

Input cell

Output cell

Input cell

Output cell

Advanced Science and Technology Letters Vol.144 (UBWCN 2017)

Copyright © 2017 SERSC 47

converter is shown in Figure 3. In the diagram, input B1 is output directly to G1 with-

out any operation. G0 is output through an

Fig. 3. A block diagram of 2 bit binary to gray code converter

Fig. 4. Abdullah’s QCA 2 bit binary to gray code converter

XOR operation between B1 and B0. When B1B0 is binary value ‘10’, output

G1G0 is ‘11’. A layout of previous QCA code converter is shown in Figure 4. The

circuit used an XOR gate in the middle of circuit and output G0’s position is located

inside. This circuit is proposed by using an OR gate and two AND gates however it

needs more wires and clocks to connect from output cell.

3 Proposed Two-Bit QCA Binary to Gray Code Converter

In this section, we proposed a QCA two-bit binary to gray code converters. In Figure

5, An XOR gate using NNI gates in the circuit are performed. As shown in Figure 5,

the outputs of a two-bit circuit are used 4 clocks. G1 is output from directly B1 and

G0 is result of XOR gate operation as shown in equation (1) and (2). The proposed

circuit is considered a scalability and low hardware complexity. We reduced cells,

cell area and designed extendable circuit. The simulation result is also shown in Fig-

ure 5. Outputs are delayed compared to inputs because of clock delay.

G1 = B1 (1)

Advanced Science and Technology Letters Vol.144 (UBWCN 2017)

48 Copyright © 2017 SERSC

G0 = B1⊕ B0 (2)

Fig. 5. Proposed two-bit binary to gray code converter in QCA

4 Comparison

In this section, we compare between previous code converter and proposed circuit as

shown in Table 1. The proposed circuit has 38 cells, area with 38,582nm2. Circuit in

[8] has bigger area and 3 clock delays in Table 1. Proposed circuit uses one more clock but the

converter in [8] needs more clocks and cells because they designed output inside circuit. Since

the output cell of the circuit in [8] is located at the center of the circuit, the scalability is de-

graded. From this perspective, we proposed high scalability and low hardware complexi-

ty circuit.

Table 1. Comparison of two-bit binary to gray code converters

Circuit Cell count Circuit area

(nm2) Clock scalability

Converter in [8] 40 45,225 3 low

Proposed

converter 38 38,582 4 high

Advanced Science and Technology Letters Vol.144 (UBWCN 2017)

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5 Conclusions

The paper has presented a low hardware complexity binary to gray code converter in

QCA. This circuit can be extended to multi bit code converter. The proposed circuit

has reduced cell count and area by using small XOR gate based on NNI gates. Com-

pare to previous circuit, our circuit has better performance. We will extend the pro-

posed circuit to large circuit and research another QCA code converter as a future

work.

Acknowledgments. This work was supported by the National Research Foundation

of Korea(NRF) grant funded by the Korea government(MSIP) (NO. NRF-

2015R1A2A1A15055749).

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Advanced Science and Technology Letters Vol.144 (UBWCN 2017)

50 Copyright © 2017 SERSC