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International Journal of Electronics

Novel designs for fault tolerant reversible binary coded decimal adders

Ri‐Gui Zhou, Yan-Cheng Li, Manqun Zhang

Published Sep 5, 2013• 31 citations
Publisher

Abstract

Reversible logic circuits have received emerging attentions in recent years. Reversible logic is widely applied in some new technical fields, such as quantum computing, nanocomputing and optical computing and so on. In this paper, three fault tolerant gates are proposed, ZPL gate, ZQC gate and ZC gate. By using the proposed gates, fault tolerant quantum and reversible BCD adder and skip carry BCD adder are designed, which overcome the limitations of the existing methods. The proposed reversible BCD adders have also parity-preserving property. They are better than the existing counterparts, especially in the quantum cost. Proposed designs have been compared with existing designs with respect to the number of gates, number of garbage outputs and quantum cost.

DOI
10.1080/00207217.2013.832388

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Reversible logic circuits have received emerging attentions in recent years. Reversible logic is widely applied in some new technical fields, such as quantum computing, nanocomputing and optical computing and so on. In this paper, three fault tolerant gates are proposed, ZPL gate, ZQC gate and ZC gate. By using the proposed gates, fault tolerant quantum and reversible BCD adder and skip carry BCD adder are designed, which overcome the limitations of the existing methods. The proposed reversible BCD adders have also parity-preserving property. They are better than the existing counterparts, especially in the quantum cost. Proposed designs have been compared with existing designs with respect to the number of gates, number of garbage outputs and quantum cost.
Reversible logic is gaining significance in the context of emerging technologies such as quantum computing since reversible circuits do not lose information during computation and there is one-to-one mapping between the inputs and outputs. In this work, we present a class of new designs for reversible binary and BCD adder circuits. The proposed designs are primarily optimized for the number of ancilla inputs and the number of garbage outputs and are designed for possible best values for the quantum cost and delay. In reversible circuits, in addition to the primary inputs, some constant input bits are used to realize different logic functions which are referred to as ancilla inputs and are overheads that need to be reduced. Further, the garbage outputs which do not contribute to any useful computations but are needed to maintain reversibility are also overheads that need to be reduced in reversible designs. First, we propose two new designs for the reversible ripple carry adder: (i) one with no input carry c 0 and no ancilla input bits, and (ii) one with input carry c 0 and no ancilla input bits. The proposed reversible ripple carry adder designs with no ancilla input bits have less quantum cost and logic depth (delay) compared to their existing counterparts in the literature. In these designs, the quantum cost and delay are reduced by deriving designs based on the reversible Peres gate and the TR gate. Next, four new designs for the reversible BCD adder are presented based on the following two approaches: (i) the addition is performed in binary mode and correction is applied to convert to BCD when required through detection and correction, and (ii) the addition is performed in binary mode and the result is always converted using a binary to BCD converter. The proposed reversible binary and BCD adders can be applied in a wide variety of digital signal processing applications and constitute important design components of reversible computing.
Over the last few decades, research in reversible logic has increasingly become very popular and it is gaining greater momentum in the present word. Reversible logic has started finding concert applications in quantum computing, optical computing, nano-technology based system, low-power CMOS design, VLSI design. The principal objective of this work is to argue for quantum implementation of various reversible logic gates by using C-NOT, Controlled-V and Controlled-V+ gates. The present work presents Binary coded decimal adder (BCD) in terms of number of gates, garbage outputs, quantum cost, delay and hardware complexity compared to existing design.
The quantum and reversible paradigm merges the principles of quantum mechanics and reversible computation to enable information-preserving processing. It supports next-generation computing architectures that provide improved scalability and enhanced computational efficiency. Within these architectures, the decimal adder is a key arithmetic component, particularly for Binary Coded Decimal (BCD) operations widely used in financial and commercial systems. However, most reversible BCD adders focus primarily on quantum and reversible metrics, overlooking the critical influence of delay, which makes balanced optimization a significant challenge. This paper presents two reversible BCD adder designs optimized for both delay and quantum cost. One design integrates the decimal carry-skip technique to improve the overall delay. Using reversible logic gates, the proposed architectures efficiently perform BCD addition and implement the required correction logic while maintaining full reversibility. Evaluation results indicate that the proposed designs surpass existing reversible BCD adders, achieving best-case average improvements of 85.12% in delay and 30.75% in quantum cost. These advancements demonstrate the potential of the proposed adders for integration into future quantum-based arithmetic units and scalable reversible computing systems. Moreover, analysis of real banking transaction data underscores the practical importance of BCD addition and its widespread use in accurate and efficient monetary computations.
Reversible logic is one of the emerging computational methodologies which assures zero power dissipation through theoretical laws of thermodynamics. It has received significant interest in application on quantum computing, nanotechnologies and low power computing devices. In this work, we present a reversible logic implementation for Binary Coded Decimal (BCD) adder which is designed to obtain lowest quantum cost value. Other parameters such as ancilla input, garbage output and delay are kept at minimal. Experiment result shows that the proposed work outperforms other designs in terms of quantum cost. Considering for a 1 digit BCD adder, it has a 4% improvement in terms of quantum cost compared to the current best existing ones. The improvement range increases as the BCD digit becomes larger.
Reversible logic is one of the emerging technologies having promising applications in quantum computing. In this work, we present new design of the reversible BCD adder that has been primarily optimized for the number of ancilla input bits and the number of garbage outputs. The number of ancilla input bits and the garbage outputs is primarily considered as an optimization criteria as it is extremely difficult to realize a quantum computer with many qubits. As the optimization of ancilla input bits and the garbage outputs may degrade the design in terms of the quantum cost and the delay, thus the quantum cost and the delay parameters are also considered for optimization with primary focus towards the optimization of the number of ancilla input bits and the garbage outputs. Firstly, we propose a new design of the reversible ripple carry adder having the input carry Co and is designed with no ancilla input bits. The proposed reversible ripple carry adder design with no ancilla input bits has less quantum cost and the logic depth (delay) compared to its existing counterparts. The existing reversible Peres gate and a new reversible gate called the TR gate is efficiently utilized to improve the quantum cost and the delay of the reversible ripple carry adder. The improved quantum design of the TR gate is also illustrated. Finally, the reversible design of the BCD adder is presented which is based on a 4 bit reversible binary adder to add the BCD number, and finally the conversion of the binary result to the BCD format using a reversible binary to BCD converter.
Within this paper, the authors introduce a new cost optimized quantum Binary-Coded Decimal (BCD) adder circuit that utilizes reversible gates as its building blocks. The newly proposed quantum BCD adder is specifically constructed with the inclusion of double Peres gates (DPG), Peres gates (PG), BJN gates, Feynman gates (FG), and reversible NOT gates. To bring this idea to life, we undertook the design and implementation of the proposed circuit using the Qiskit simulator provided by the IBM Quantum Computing lab. Our evaluation of the newly optimized BCD adder circuit yielded the following metrics, the quantum cost of 47, the constant input of 8, garbage output of 12, and a delay of 10. When compared to previously reported results, we observed significant improvements in various aspects, with a 25.39% reduction in quantum cost, a 28.57% decrease in constant input, and a 36.84% reduction in garbage output.