Microelectronics Journal 39 (2008) 1693– 1703

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Microelectronics Journal

journal homepage: www.elsevier.com/locate/mejo

Efﬁcient approaches for designing reversible Binary Coded Decimal adders Ashis Kumer Biswas, Md. Mahmudul Hasan, Ahsan Raja Chowdhury, Haﬁz Md. Hasan Babu Ã Department of Computer Science and Engineering, University of Dhaka, Dhaka 1000, Bangladesh

a r t i c l e in fo

Article history: Received 27 November 2007 Received in revised form 5 April 2008 Accepted 16 April 2008 Available online 18 June 2008 Keywords: Reversible logic Garbage output Gate complexity Binary Coded Decimal adder Carry Skip BCD adder Quantum cost

abstract

Reversible logic has become one of the most promising research areas in the past few decades and has found its applications in several technologies; such as low-power CMOS, nanocomputing and optical computing. This paper presents improved and efﬁcient reversible logic implementations for Binary Coded Decimal (BCD) adder as well as Carry Skip BCD adder. It has been shown that the modiﬁed designs outperform the existing ones in terms of number of gates, number of garbage outputs, delay, and quantum cost. In order to show the efﬁciency of the proposed designs, lower bounds of the reversible BCD adders in terms of gates and garbage outputs are proposed as well. & 2008 Elsevier Ltd. All rights reserved.

1. Introduction The advancement in higher-level integration and fabrication process has emerged in better logic circuits and energy loss has also been dramatically reduced over the last decades. This trend of reduction of heat in computation also has its physical limit. According to Landauer [1,2], in logic computation every bit of information loss generates kTln2 joules of heat energy where k is Boltzmann’s constant of 1.38 Â 10À23 J/K and T is the absolute temperature of the environment. At room temperature, the dissipating heat is around 2.9 Â 10À21 J. Energy loss due to Landauer limit is also important as it is likely that the growth of heat generation causing information loss will be noticeable in future. Reversible circuits are fundamentally different from traditional irreversible ones. In reversible logic, no information is lost, i.e. the circuit that does not lose information is reversible. Bennett [3] showed that zero energy dissipation would be possible if the network consists of reversible gates only. Thus, reversibility will be an essential property for the future circuit design. Quantum computation is also gaining popularity as some exponentially hard problems can be solved in polynomial time [4]. We know that quantum computation is reversible. Thus, research in reversible logic is helpful for the development of future technologies; it has the potential to methods of quantum circuit construction resulting in more powerful computers. Quantum technology is not the only one where reversibility is used.

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E-mail address: haﬁzbabu@hotmail.com (H.M. Hasan Babu). 0026-2692/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2008.04.003

Reversible logic has also found its applications in several other disciplines such as nanotechnology [5], DNA technology [6] and optical computing [7]. In computers, numbers are stored in straight binary format. Due to inherent characteristics of ﬂoating-point numbers and limitations on storing formats, not all ﬂoating-point numbers can be represented with desired precision [8]. So, computing in decimal format is gaining popularity as loss due to precision can be avoided in this format. However, hardware support for binary arithmetic allows it to be performed faster than decimal arithmetic. Faster hardware for decimal ﬂoating-point arithmetic is also imminent as it has its importance in ﬁnancial and Internet based applications. So, faster circuits for Binary Coded Decimal...