This paper proposes two reversible logic gates, HNFG and HNG. The first gate HNFG can be used as two Feynman Gates. It is suitable for a single copy of two bits with no garbage outputs. It can be used as &#34Copying Circuit&#34 to increase fan-out because fan-out is not allowed in reversible circuits. The second gate HNG can implement all Boolean functions. It also can be used to design optimized adder architectures. This paper also proposes a novel reversible full adder. One of the prominent functionalities of the proposed HNG gate is that it can work singly as a reversible full adder unit. The proposed reversible full adder contains only one gate. We show that its hardware complexity is less than the existing reversible full adders. The proposed full adder is then applied to the design of a reversible 4-bit parallel adder. A reversible Binary Coded Decimal (BCD) adder circuit is also proposed. The proposed circuit can add two 4-bit binary variables and it transforms the result into the appropriate BCD number using efficient error correction modules. We show that the proposed reversible BCD adder has lower hardware complexity and it is much better and optimized in terms of number of reversible gates and garbage outputs with compared to the existing counterparts.

A Novel Reversible BCD Adder For Nanotechnology Based Systems

Designing efficient QCA logical circuits with power dissipation analysis

Five figures of merit including number of gates, quantum cost, number of constant inputs, number of garbage outputs, and delay are used casually in the literature to compare the performance of different reversible or quantum logic circuits. In this paper we propose new definitions and enhancements, and identify similarities between these figures of merit. We evaluate these measures to show their strength and weakness. Instead of the number of gates, we introduce the weighted number of gates, where a weighting factor is assigned to each quantum or reversible gate, based on its type, size and technology. We compare the quantum cost with weighted number of gates of a circuit and show three major differences between these measures. It is proved that it is not possible to define a universal reversible logic gate without adding constant inputs. We prove that there is an optimum value for number of constant inputs to obtain a circuit with minimum quantum cost. Some reversible logic benchmarks have been synthesized using Toffoli and Fredkin gates to obtain their optimum values of number of constant inputs. We show that the garbage outputs can also be used to decrease the quantum cost of the circuit. A new definition of delay in quantum and reversible logic circuits is proposed for music line style representation. We also propose a procedure to calculate the delay of a circuit, based on the quantum cost and the depth of the circuit. The results of this research show that to achieve a fair comparison among designs, figures of merit should be considered more thoroughly.

On figures of merit in reversible and quantum logic designs

Efficient approaches for designing reversible Binary Coded Decimal adders

Modular Design of testable reversible ALU by QCA multiplexer with increase in programmability

In this paper, we propose the design of two vectors testable sequential circuits based on conservative logic gates. The proposed sequential circuits based on conservative logic gates outperform the sequential circuits implemented in classical gates in terms of testability. Any sequential circuit based on conservative logic gates can be tested for classical unidirectional stuck-at faults using only two test vectors. The two test vectors are all 1's, and all 0's. The designs of two vectors testable latches, master-slave flip-flops and double edge triggered (DET) flip-flops are presented. The importance of the proposed work lies in the fact that it provides the design of reversible sequential circuits completely testable for any stuck-at fault by only two test vectors, thereby eliminating the need for any type of scan-path access to internal memory cells. The reversible design of the DET flip-flop is proposed for the first time in the literature. We also showed the application of the proposed approach toward 100% fault coverage for single missing/additional cell defect in the quantum-dot cellular automata (QCA) layout of the Fredkin gate. We are also presenting a new conservative logic gate called multiplexer conservative QCA gate (MX-cqca) that is not reversible in nature but has similar properties as the Fredkin gate of working as 2:1 multiplexer. The proposed MX-cqca gate surpasses the Fredkin gate in terms of complexity (the number of majority voters), speed, and area.

Design of Testable Reversible Sequential Circuits

IEEE 754r is the ongoing revision to the IEEE 754 floating point standard and a major enhancement to the standard is the addition of decimal format. This paper proposes two novel BCD adders called carry skip and carry look-ahead BCD adders respectively. Furthermore, in the recent years, reversible logic has emerged as a promising technology having its applications in low power CMOS, quantum computing, nanotechnology, and optical computing. It is not possible to realize quantum computing without reversible logic. Thus, this paper also paper provides the reversible logic implementation of the conventional BCD adder as the well as the proposed Carry Skip BCD adder using a recently proposed TSG gate. Furthermore, a new reversible gate called TS-3 is also being proposed and it has been shown that the proposed reversible logic implementation of the BCD Adders is much better compared to recently proposed one, in terms of number of reversible gates used and garbage outputs produced. The reversible BCD circuits designed and proposed here form the basis of the decimal ALU of a primitive quantum CPU.

Novel BCD Adders and Their Reversible Logic Implementation for IEEE 754r Format

IEEE 754r is the ongoing revision to the IEEE 754 floating point standard and a major enhancement to the standard is the addition of decimal format. This paper proposes two novel BCD adders called carry skip and carry look-ahead BCD adders respectively. Furthermore, in the recent years, reversible logic has emerged as a promising technology having its applications in low power CMOS, quantum computing, nanotechnology, and optical computing. It is not possible to realize quantum computing without reversible logic. Thus, this paper also paper provides the reversible logic implementation of the conventional BCD adder as the well as the proposed carry skip BCD adder using a recently proposed TSG gate. Furthermore, a new reversible gate called TS-3 is also being proposed and it has been shown that the proposed reversible logic implementation of the BCD adders is much better compared to recently proposed one, in terms of number of reversible gates used and garbage outputs produced. The reversible BCD circuits designed and proposed here form the basis of the decimal ALU of a primitive quantum CPU.

Novel BCD adders and their reversible logic implementation for IEEE 754r format

Reversible logic has emerged as a promising computing paradigm having applications in quantum computing, optical computing, dissipation less computing and low power computing etc. In reversible logic there exists a one to one mapping between the input and output vectors. Reversible circuits require constant ancilla inputs for reconfiguration of gate functions and garbage outputs that help in keeping reversibility. Quantum circuits of many qubits are extremely difficult to realize thus reduction in the number of ancilla inputs and the garbage outputs is the primary goal of optimization. In existing literature researchers have proposed several designs of reversible quantum multipliers based on reversible full adders and reversible half adders. The use of reversible full adders and the half adders for the addition of partial products increases the overhead in terms of number of ancilla inputs and number of garbage outputs. This paper presents a binary tree based design methodology for a NxN reversible quantum multiplier. The proposed binary tree based design methodology for NxN reversible quantum multiplier performs the addition of partial products in parallel using the reversible ripple quantum adders with no garbage output and ancilla bit, thereby minimizing the number of ancilla and garbage bits used in the design. The proposed design methodology shows the improvement of 17.86% to 60.34% in terms of ancilla inputs; and 21.43% to 52.17% in terms of garbage outputs compared to all the existing reversible quantum multiplier designs.

Circuit for Reversible Quantum Multiplier Based on Binary Tree Optimizing Ancilla and Garbage Bits

In recent years reversible logic has emerged as a promising computing model for applications in dissipation less optical computing, low power CMOS, quantum computing, etc. In reversible circuits there exist a one-to-one mapping between the inputs and the outputs resulting in no loss of information. Researchers have implemented reversible logic gates in optical computing domain as it can provide high speed and low energy requirement along with easy fabrication at the chip level [1]. The all optical implementation of reversible gates are based on semiconductor optical amplifier (SOA) based Mach-Zehnder interferometer (MZI) due to its significant advantages such as high speed, low power, fast switching time and ease in fabrication. In this work we present the all optical implementation of an n bit reversible ripple carry adder for the first time in literature. The all optical reversible adder design is based on two new optical reversible gates referred as optical reversible gate I (ORG-I) and optical reversible gate II (ORG-II) and the existing all optical Feynman gate. The two new reversible gates ORG-I and ORGI-I are proposed as they can implement a reversible adder with reduced optical cost which is the measure of number of MZIs switches and the propagation delay, and with zero overhead in terms of number of ancilla inputs and the garbage outputs. The proposed all optical reversible adder design based on the ORG-I and ORG-II reversible gates are compared and shown to be better than the other existing designs of reversible adder proposed in non-optical domain in terms of number of MZIs, delay, number of ancilla inputs and the garbage outputs. The proposed all optical reversible ripple carry adder will be a key component of an all optical reversible ALU that can be applied in a wide variety of optical signal processing applications.

Saurabh Kotiyal

Papers

Design of Testable Reversible Sequential Circuits

Novel BCD Adders and Their Reversible Logic Implementation for IEEE 754r Format

Novel BCD adders and their reversible logic implementation for IEEE 754r format

Circuit for Reversible Quantum Multiplier Based on Binary Tree Optimizing Ancilla and Garbage Bits

Mach-zehnder interferometer based design of all optical reversible binary adder