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An Approach for Realization of 2's Complement Adder Subtractor Using DKG Reversible Gate

Shefali Mamataj, Biswajit Das, Anurima Rahaman

Published Jan 1, 2013• 6 citations
OpenAlex

Abstract

Abstract — Reversible logic is one of the most important issue at present time and it has different areas for its application. The main purposes of designing reversible logic are to decrease quantum cost, depth of the circuits and the number of garbage outputs This paper represents an another approach to realize 4 bit 2’s complement adder subtractor by using reversible logic gates like Feynman Gate, DKG gate and one control line. A also a new reversible gate DKFG is proposed. Keywords—Reversible logic, Basic Reversible Gates, 2’s Complement, Reversible full adder, Reversible full sub-

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Abstract — Reversible logic is one of the most important issue at present time and it has different areas for its application. The main purposes of designing reversible logic are to decrease quantum cost, depth of the circuits and the number of garbage outputs This paper represents an another approach to realize 4 bit 2’s complement adder subtractor by using reversible logic gates like Feynman Gate, DKG gate and one control line. A also a new reversible gate DKFG is proposed. Keywords—Reversible logic, Basic Reversible Gates, 2’s Complement, Reversible full adder, Reversible full sub-
The power consumption in classical computers has grown to be a critical issue. Thus, quantum computers have become a promising alternative to classical computers for more processing power and lower energy consumption. Reversible gates are important for building the quantum computers. Reversible circuits have various applications, such as digital signal processing, optical computing, quantum computing, etc. The design and synthesis of reversible gates and circuits have grown in popularity and attracted the attention of many researchers. The adder and subtractor are important computation blocks for the structure of the Arithmetic Logic Unit (ALU). In this paper, a design of reversible binary half and full adders and subtractors using reversible logic gates is proposed. The TR (Thapliyal Ranganathan) and Peres gates are used to construct the reversible half adder and subtractor circuit. Meanwhile, the Double Peres Gate (DPG), Fredkin, and NOT gates are used to build the reversible 1-bit full adder and subtractor circuit. The designs are optimized in terms of number of gates, constant inputs, garbage outputs, and quantum cost. The truth table representation and the Binary Decision Diagram (BDD) synthesis method are used to represent and synthesize the circuits, respectively. The circuits are synthesized and simulated using the Verilog Hardware Description Language code and Xilinx ISE 14.7. The results show that the proposed designs achieve the lowest quantum cost in both half adder/subtractor and full adder/subtractor. As the half adder/subtractor has six quantum cost and the full adder/subtractor has nine quantum cost.
Abstract — Reversible logic is one of the most vital issue at present time and it has different areas for its application, those are low power CMOS, quantum computing, nanotechnology, cryptography, optical computing, DNA computing, digital signal processing (DSP), quantum dot cellular automata, communication, computer graphics. It is not possible to realize quantum computing without implementation of reversible logic. The main purposes of designing reversible logic are to decrease quantum cost, depth of the circuits and the number of garbage outputs. This paper provides the basic reversible logic gates, which in designing of more complex system having reversible circuits as a primitive component and which can execute more complicated operations using quantum computers. The reversible circuits form the basic building block of quantum computers as all quantum operations are reversible. This paper presents the data relating to the primitive reversible gates which are available in literature and helps researches in designing higher complex computing circuits using reversible gates.
This paper proposed the design and development of reversible cost-efficient innovative quantum dual-full adder and subtractor or QD-FAS circuit using quantum gate. The proposed circuit can be used as full adder and full subtractor simultaneously, which is designed using double Peres gate or DPG and Feynman gate or FG. The quantum cost, garbage output and constant input of the QD-FAS is 8, 1 and 1. Which is better w.r.t previously reported work. The QD-FAS circuit, as proposed, includes shared sum and difference terminals, as well as a carry-out and a borrow output terminal. Notably, this innovation showcases a remarkable 27.27% reduction in quantum cost. The improvement in garbage output is even more striking, showing a 50% enhancement. When assessing the overall advancement in quantum cost, it falls within the range of 27.27% to 66.66%. To confirm the viability of this design, extensive testing is carried out using the IBM Qiskit simulator. This design holds significant importance in a variety of applications, including quantum computing, cryptography, and the realm of reversible Arithmetic Logic Units (ALU).
Reversible logic gates are essential for quantum computing and low-power digital circuits as they enable the recovery of input signals from output signals, thereby minimizing energy dissipation. This field of study has become a leading-edge research domain, driving innovative advancements focused on optimizing resource efficiency. This study introduces an efficient 8-bit adder/subtractor circuit designed using Feynman and HNG reversible logic gates. The circuit incorporates a control bit (M) that dictates its operational mode: M=0 signifies addition functionality, while M=1 indicates subtraction functionality. This dual functionality is achieved with substantial efficiency enhancements, as evidenced by a 22% decrease in quantum cost compared to traditional methods. The design also boasts a reduced total reversible logic implementation cost, underscoring its efficiency. Validation and simulation of the reversible 8-bit adder/subtractor circuit are conducted using Xilinx Vivado 2022.2 software