Logic Optimization for Majority Gate-Based Nanoelectronic Circuits Based on Genetic Algorithm M.R. Bonyadi 1 ,S.M.R. Azghadi 2 , N.M. Rad 3 , K. Navi 4 and E. Afjei 5 , Department of Electrical & Computer Engineering, Shahid Beheshti University, Tehran, Iran 1 M_bonyadi@std.sbu.ac.ir, 2 m_rahimi@std.sbu.ac.ir Abstract- In this paper we propose a novel and efficient method for majority gate-based design. The basic Boolean primitive in quantum cellular automata (QCA) is the majority gate. Method for reducing the number of majority gates required for computing Boolean functions is developed to facilitate the conversion of Sum Of Products (SOP) expression into QCA majority logic. This method is based on genetic algorithm and can reduce the hardware requirements for a QCA design. We will show that the proposed approach is very efficient in deriving the simplified majority expression in QCA design. Key words: majority expression, Genetic Algorithm, QCA, hardware reduction. I. INTRODUCTION Nanodevices such as quantum cellular automata (QCA), tunneling phase logic (TPL) and single electron tunneling (SET) are possible candidates for post-CMOS IC designs [1,2]. The basic building block of QCA circuit is majority gate, hence, efficiently constructing QCA circuits using majority gates has attracted a lot of attentions [2,3]. Related study goes back to 1960s [4]. Recently, a comprehensive QCA majority synthesis method has been introduced based on a multi-level mapping approach. In implementation of any logical function with majority, instead of using Boolean logic operators (AND, OR, and their complements), majority logic represents and manipulates digital functions on the basis of majority decision[5]. By using an optimization based on GA, we reduce the number of both majority gates and inverters. The optimizer is implemented in C# language and the experimental results are obtained and compared with recent available results [3,9]. The proposed method can be easily extended to minority-based circuit such as TPL and SET. II. BACKGROUND MATERIALS A. Nanoelectronic Circuit based on Majority gate Any QCA circuit can be efficiently built using only majority gates and inverters. As shown in Fig. 1 (a), a QCA gate implementing the majority function is as follows. M (A,B,C)=AB+BC+AC (1) (a) (b) Fig. 1, (a) A QCA majority gate (b) A QCA inverter As you can see in Fig.1 (a and b), each QCA majority gate requires only five QCA cells. And every QCA inverter gate can be implemented by 13 quantum cells. As it is shown in (2a) and (2b), for generating an AND gate or an OR gate with majority we can fix the polarization of one input to a constant logic ‘0’ or logic ‘1’. Hence, QCA circuit is based on majority gate-based circuits instead of AND/OR/Inverter gate-based circuits [1,2]. M(A,B,0)=AB (2a) M(A,B,1)=A+B (2b) Therefore, reducing the number of both majority gates and inverters is to be considered in the logic synthesis of QCA circuits. B. Majority Gate-Based Logic synthesis The logic process of majority logic is much more sophisticated than that of Boolean logic[5]. Recently, researches on the majority/minority synthesis has attracted a lot of attentions [1,2]. The most recent works are [2,6,9], which can be considered as the first comprehensive method for multi-level majority network synthesis. C. Genetic Algorithm (GA) Genetic Algorithms [7,8] (GAs) have long been investigated as a possible solution for many search and optimization problems. GAs are evolutionary algorithms that mimic the way nature improves the characteristics of living beings. Each solution (individual) is represented as a string (chromosome) of elements (genes) and is assigned a fitness value based on the value given by an evaluation 1-4244-0893-8/07/$20.00 ©2007 IEEE