Digital multipliers are indispensable in Digital signal processing and cryptography. In many mathematical computations, squaring and cubing are frequently used. Generally the multiplier is used in computing square. But the implementation of squaring has the advantage that we can avoid the generation of many partial products used in multipliers by eliminating the redundant bits, thus resulting the circuit to be simpler with less hardware, propagation delay and power consumption. Our work proposes two designs of dedicated squaring techniques in reversible circuits. We use the recursion to achieve our design. The design for n bits is recursively obtained by appending some extra circuitry with the design for (n-1) bits. Our techniques make optimum use of ancillary inputs, garbage outputs and quantum cost and compare favourably with the recent work [1] in this area. Both the designs are having modular structures and can be systemically designed.
Digital multipliers are indispensable in Digital signal processing and cryptography. In many mathematical computations, squaring and cubing are frequently used. Generally the multiplier is used in computing square. But the implementation of squaring has the advantage that we can avoid the generation of many partial products used in multipliers by eliminating the redundant bits, thus resulting the circuit to be simpler with less hardware, propagation delay and power consumption. Our work proposes two designs of dedicated squaring techniques in reversible circuits. We use the recursion to achieve our design. The design for n bits is recursively obtained by appending some extra circuitry with the design for (n-1) bits. Our techniques make optimum use of ancillary inputs, garbage outputs and quantum cost and compare favourably with the recent work [1] in this area. Both the designs are having modular structures and can be systemically designed.
Quantum computation is modeled by quantum circuits. All the quantum operations are reversible so the quantum circuits can be built using reversible logic gates. Reversible computing is the emerging technology, its major role is in the field of quantum computing, optical computing, and design of low power nanocircuits. The most frequently used computational unit for digital signal processing and multimedia applications is multiplier. To compute square of an operand, regular multipliers are used in general. This paper proposes a dedicated quantum circuit for computing square of an operand efficiently compared to the existing multipliers in the literature. The squaring unit is mathematically modeled and its metrics quantum cost, garbage outputs and ancilla input, gate count are calculated. We compared the proposed design with the existing multipliers to compute square and found that proposed square unit is efficient in terms of quantum cost, garbage outputs, ancilla inputs and gate count. The proposed reversible square circuit has 63% to 85% improvement of quantum cost, garbage outputs, ancilla inputs and gate count over existing reversible multiplier circuits.
In this paper, our objective is to design an efficient dedicated squaring architecture in reversible logic using reduced ancillary inputs and zero garbage outputs. The proposed design has a modular structure and has been built recursively. The quantum cost optimization has been achieved using NCV-|1 > and NCV-|v1> and double gate libraries. The performance parameters like ancillary inputs, garbage outputs and quantum cost have been formulated from the design and compared with a very recent work [1].
Reversible logic circuits have received significant attention in quantum computing, low power CMOS design, optical information processing, DNA computing, bioinformatics, and nanotechnology. This paper presents two new 4 × 4 bit reversible multiplier designs which have lower hardware complexity, less garbage bits, less quantum cost and less constant inputs than previous ones, and can be generalized to construct efficient reversible n × n bit multipliers. An implementation of reversible HNG is also presented. This implementation shows that the full adder design using HNG is one of the best designs in term of quantum cost. An implementation of MKG is also presented in order to have a fair comparison between our proposed reversible multiplier designs and the existing counterparts. The proposed reversible multipliers are optimized in terms of quantum cost, number of constant inputs, number of garbage outputs and hardware complexity. They can be used to construct more complex systems in nanotechnology.
Reversible logic is leading area in power consumption.Based on its application, its emerging trend in power consumption.In ideal situations, reversible circuit yield nil power.Different methods of multiplier optimized in this paper.Like quantum computers, multipliers required to develop computational units.In the paper, two different methods of multiplier developed with very large bit width.Based on partial products hierarchical method is developed.Another method is Karatsuba's algorithm developed based on divide and conquers method.Finally, we compare the results of both two methods.The projected reversible multipliers are enhanced in terms of quantum cost, number of constant inputs, number of garbage outputs and complexity in hardware.In nanotechnology applications this multiplier can be used to construct complex system.
There are many arithmetic operations which are performed, on a computer arithmetic unit, through the use of multipliers (e.g., exponential and trigonometric functions). Consequently, optimized multipliers are on demand while designing an arithmetic unit. On the other hand, given the advent of quantum computer and reversible logic, design and implementation of digital circuits in this logic has gained popularity. In reversible circuit design, decreasing three parameters is of interest: quantum cost, depth of the circuit and the number of garbage outputs. In this paper, we propose a novel reversible multiplier with the aim of decreasing the depth of the circuit while neither scarifying any extra quantum cost nor garbage outputs. The partial products, as is the case for prior works, are generated in parallel using Peres gates and thereafter a reversible multi-operand adder consisting of reversible full-adders and half-adders produces the final product.
Reversible logic is one of the stepping stones in low power circuit design. Due to low power consumption and minimum bit loss features, future quantum computing devices are estimated to be reversible. Compared to addition, multiplication is a step further in the ladder of abstraction. It is the manifestation of a pattern generation system capable of representing 3-D patterns and transforming them by rotation, projection, reflection etc. The use of reversible logic in this field can reduce the wastage of energy, power and improve many factors. In this paper, an efficient multiplication algorithm has been proposed which is a modification of conventional shift-and-add multiplication method. Implementing proposed algorithm two reversible multiplier circuit has been proposed. For producing partial product, Peres gate has been used for the first design and Toffoli gate for the second design. Both of the circuits use Peres gate as Half-Adder and HNG gate as Full-Adder for addition of partial products. The first design is improved radically in terms of quantum cost, delay and the second design is notably improved in terms of transistor count and hardware complexity compared to the existing best known multipliers.