Novel parity-preserving reversible logic array multipliers

Reversible logic as a new promising design domain can be used for DNA computations, nanocomputing, and especially constructing quantum computers. However, the vulnerability to different external effects may lead to deviation from producing correct results. The multiplication is one of the most important operations because of its huge usage in different computing systems. Thus, in this paper, some novel reversible logic array multipliers are proposed with error detection capability through the usage of parity-preserving gates. By utilizing the new arrangements of existing reversible gates, some new circuits are presented for partial product generation and multi-operand addition required in array multipliers which results in two unsigned and three signed parity-preserving array multipliers. The experimental results show that the best of signed and unsigned proposed multipliers have the lowest values among the existing designs regarding the main reversible logic criteria including quantum cost, gate count, constant inputs, and garbage outputs. For \(4\times 4\) multipliers, the proposed designs achieve up to 28 and 46% reduction in the quantum cost and gate count, respectively, compared to the existing designs. Moreover, the proposed unsigned multipliers can reach up to 58% gate count reduction in \(16\times 16\) multipliers.     

Design of a reversible floating-point square root using modified non-restoring algorithm

In this work, a reversible single precision floating-point square root is proposed using modified non-restoring algorithm. To our knowledge, this is the first work proposed for floating-point square root using reversible logic. The main block involved in the implementation of reversible square root using modified non-restoring technique is Reversible Controlled-Subtract-Multiplex. Further, optimized Reversible Controlled-Subtract-Multiplex blocks are introduced in order to minimize the number of reversible gates used, number of constant inputs used, number of garbage outputs produced as well as the quantum cost. The proposed reversible single precision floating-point square root is realized using an 8-bit reversible adder, an 8-bit and a 25-bit reversible shift register, 12-bit reversible unsigned square root, 6-bit reversible unsigned square root, 4-bit reversible unsigned square root, 3-bit reversible unsigned square root and ten 1-bit reversible unsigned square root units.     

Toward novel designs of reversible ternary 6:2 Compressor using efficient reversible ternary full-adders

Integrated circuits always face with two major challenges including heat caused by energy losses and the area occupied. In recent years, different strategies have been presented to reduce these two major challenges. The implementations of circuits in a reversible manner as well as the use of multiple-valued logic are among the most successful strategies. Reversible circuits reduce energy loss and ultimately eliminate the problem of overheating in circuits. Preferring multiple-valued logic over binary logic can also greatly reduce area occupied of circuits. When switching from binary logic to multiple-valued logic, the dominant thought in binary logic is the basis of designing computational circuits in multiple-valued logic, and disregards the capabilities of multiple-valued logic. This can cause a minimal use of multiple-valued logic capabilities, increase complexity and delay in the multiple-valued computational circuits. In this paper, we first introduce an efficient reversible ternary half-adder. Afterward, using the reversible ternary half-adder, we introduce two reversible versions of traditional and comprehensive reversible ternary full-adders. Finally, using the introduced reversible ternary full-adders, we propose two novel designs of reversible ternary 6:2 Compressor. The results of the comparisons show that although the proposed circuits are similar to or better than previous corresponding designs in terms of criteria number of constant input and number of garbage outputs, they are superior in criterion quantum cost.

     

A novel power efficient 0.64-GFlops fused 32-bit reversible floating point arithmetic unit architecture for digital signal processing applications

Floating point digital signal processing technology has become the primary method for real time signal processing in most digital systems presently. However, the challenges in the implementation of floating point arithmetic on FPGA are that, the hardware modules are larger, have longer latency and high power consumption. In this work, a novel efficient reversible floating point fused arithmetic unit architecture is proposed confirming to IEEE 754 standard. By utilizing reversible logic circuits and implementation with adiabatic logic, power efficiency is achieved. The hardware complexity is reduced by employing fused elements and latency is improved by decomposing the operands in the realization of floating point multiplier and square root. To validate the design, the proposed unit was used for realization of FFT and FIR filter which are important applications of a DSP processor. As detection is one of the core baseband processing operations in digital communication receivers and the detection speed determines the data rates that can be achieved, the proposed unit has been used to implement the detection function. Simulation results and comparative studies with existing works demonstrate that the proposed unit efficiently utilizes the number of gates, has reduced quantum cost and produced less garbage outputs with low latency, thereby making the design a computational and power efficient one.     

量子可逆逻辑电路综合的快速算法研究

可逆逻辑有许多应用,尤其在量子计算领域,量子可逆逻辑电路是构建量子计算机的基本单元,量子可逆逻辑电路综合就是根据电路功能,以较小的量子代价自动构造量子可逆逻辑电路.文中结合可逆逻辑电路综合的多种算法,提出了一种新颖高效的算法,自动构造正极性Reed-Muller展开式(RM),在生成量子可逆逻辑电路的解空间树上,采用总体层次遍历,局部深度搜索,借鉴模板优化技术,构造限界函数快速剪去无解或非最优解的分枝,优先探测RM中的因子,以极高的效率生成最优电路.以国际公认的3变量可逆函数测试标准,该算法不仅能够生成全部最优电路,而且运行速度远远超过同类算法.     

Novel designs of nanometric parity preserving reversible compressor

Reversible logic is a new field of study that has applications in optical information processing, low power CMOS design, DNA computing, bioinformatics, and nanotechnology. Low power consumption is a basic issue in VLSI circuits today. To prevent the distribution of errors in the quantum circuit, the reversible logic gates must be converted into fault-tolerant quantum operations. Parity preserving is used to realize fault tolerant in this circuits. This paper proposes a new parity preserving reversible gate. We named it NPPG gate. The most significant aspect of the NPPG gate is that it can be used to produce parity preserving reversible full adder circuit. The proposed parity preserving reversible full adder using NPPG gate is more efficient than the existing designs in term of quantum cost and it is optimized in terms of number of constant inputs and garbage outputs. Compressors are of importance in VLSI and digital signal processing applications. Effective VLSI compressors reduce the impact of carry propagation of arithmetic operations. They are built from the full adder blocks. We also proposed three new approaches of parity preservation reversible 4:2 compressor circuits. The third design is better than the previous two in terms of evaluation parameters. The important contributions have been made in the literature toward the design of reversible 4:2 compressor circuits; however, there are not efforts toward the design of parity preservation reversible 4:2 compressor circuits. All the scales are in the nanometric criteria.     

Novel low power reversible binary incrementer design using quantum-dot cellular automata

This paper demonstrates the design of n-bit novel low power reversible binary incrementer in Quantum-Dot Cellular Automata (QCA). The comparison of quantum cost in quantum gate based approach and in QCA based design agreed the cost efficient implementation in QCA. The power dissipation by proposed circuit is estimated, which shows that the circuit dissipates very low heat energy suitable for reversible computing. All the circuits are evaluated in terms of logic gates, circuit density and latency that confirm the faster operating speed at nano scale. The reliability of the circuit under thermal randomness is explored which describes the efficiency of the circuit.     

一种高性能子字并行乘法器的设计与实现

提出了一种支持子字并行的乘法器体系结构,并完成了其VLSI设计与实现。该乘法器在16 bit阵列子字并行结构的基础上,扩展了有符号与无符号之间的混合操作,采用多周期合并技术,实现了32 bit宽度的子字并行,并支持子字模式的乘累加,同时采用流水线设计技术,能够在单周期内完成4个8×8、2个16×16或1个32×16的有符号/无符号乘法操作。0.18 μm的标准单元库的实现表明该乘法器既能减小面积又能提高主频,是硬件消耗和运算性能的较好折衷,非常适用于多媒体微处理器的设计。     

Design and implementation of low power and high speed multiplier using quaternary carry look-ahead adder

Need of Digital Signal Processing (DSP) systems which is embedded and portable has been increasing as a result of the speed growth of semiconductor technology. Multiplier is a most crucial part in almost every DSP application. So, the low power, high speed multipliers is needed for high speed DSP. Array multiplier is one of the fast multiplier because it has regular structure and it can be designed very easily. Array multiplier is used for multiplication of unsigned numbers by using full adders and half adders. It depends on the previous computations of partial sum to produce the final output. Hence, delay is more to produce the output. In the previous work, Complementary Metal Oxide Semiconductor (CMOS) Carry Look-ahead Adders (CLA) and CMOS power gating based CLA are used for maximizing the speed of the multiplier and to improve the power dissipation with minimum delay. CMOS logic is based on radix 2(binary) number system. In arithmetic operation, major issue corresponds to carry in binary number system. Higher radix number system like Quaternary Signed Digit (QSD) can be used for performing arithmetic operations without carry. The proposed system designed an array multiplier with Quaternary Signed Digit number system (QSD) based Carry Look-Ahead Adder (CLA) to improve the performance. Generally, the quaternary devices require simpler circuit to process same amount of data than that needed in binary logic devices. Hence the Quaternary logic is applied in the CLA to improve the speed of adder and high throughput. In array multiplier architecture, instead of full adders, carry look-ahead adder based on QSD are used. This facilitates low consumption of power and quick multiplication. Tanner EDA tool is used for simulating the proposed multiplier circuit in 180 nm technology. With respect to area, Power Delay Product (PDP), Average power proposed QSD CLA multiplier is compared with Power gating CLA and CLA multiplier.     

On figures of merit in reversible and quantum logic designs

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.      

Algorithm and Implementation of Parallel Multiplication in a Mixed Number System

This paper presents a high-speed multiplication algorithm for the mixed number system of the ordinarybinary number and the symmetric redundant binary number.It is implemented with the multivalned logictheory,and 3-valued and 2-valued circuits are used.The 3-valued circuit proposed in this paper is anemitter-coupled logic circuit with high speed,simplicity and powerful functions.A 3-valued ECL thresholdgate can simultaneously produce six types of one-variable operations.The array multiplier,designed withthe algorithm and the circuits,is fast and simple,and is suitable for building LSI.It can be used in a high-speed computer just as an ordinary binary multiplier.     

Designing new ternary reversible subtractor circuits

The reducing of the width of quantum reversible circuits makes multiple-valued reversible logic a very promising research area. Ternary logic is one of the most popular types of multiple-valued reversible logic, along with the Subtractor, which is among the major components of the ALU of a classical computer and complex hardware. In this paper the authors will be presenting an improved design of a ternary reversible half subtractor circuit. The authors shall compare the improved design with the existing designs and shall highlight the improvements made after which the authors will propose a new ternary reversible full subtractor circuit. Ternary Shift gates and ternary Muthukrishnan–Stroud gates were used to build such newly designed complex circuits and it is believed that the proposed designs can be used in ternary quantum computers. The minimization of the number of constant inputs and garbage outputs, hardware complexity, quantum cost and delay time is an important issue in reversible logic design. In this study a significant improvement as compared to the existing designs has been achieved in as such that with the reduction in the number of ternary shift and Muthukrishnan-Stroud gates used the authors have produced ternary subtractor circuits.     

基于Hash表的量子可逆逻辑电路综合的快速算法

量子可逆逻辑电路是构建量子计算机的基本单元,通过量子门的级联与组合构成量子计算机,量子可逆逻辑电路的综合就是根据电路功能,以较小的量子代价自动构造量子可逆逻辑电路.结合可逆逻辑电路综合的多种算法,提出了一种新颖高效的量子电路综合算法,巧妙构造最小完备的Hash函数,可使用多种量子门,采用任意量子代价标准,以极高的效率生成最优的量子可逆逻辑电路.为实现量子电路综合的自动化,首次提出了利用量子线的置换自动构造各种量子门库的通用算法.采用国际同行认可的3变量可逆函数测试标准,该算法不仅能够生成全部最优电路.而且运行速度远远超过其他算法·实验结果表明,该算法按最小长度、最小代价标准综合电路的平均速度分别是目前最好结果的49.15倍、365.13倍.     

Reversible binary subtractor design using quantum dot-cellular automata

In the field of nanotechnology, quantum dot-cellular automata (QCA) is the promising archetype that can provide an alternative solution to conventional complementary metal oxide semiconductor (CMOS) circuit. QCA has high device density, high operating speed, and extremely low power consumption. Reversible logic has widespread applications in QCA. Researchers have explored several designs of QCA-based reversible logic circuits, but still not much work has been reported on QCA-based reversible binary subtractors. The low power dissipation and high circuit density of QCA pledge the energy-efficient design of logic circuit at a nano-scale level. However, the necessity of too many logic gates and detrimental garbage outputs may limit the functionality of a QCA-based logic circuit. In this paper we describe the design and implementation of a DG gate in QCA. The universal nature of the DG gate has been established. The QCA building block of the DG gate is used to achieve new reversible binary subtractors. The proposed reversible subtractors have low quantum cost and garbage outputs compared to the existing reversible subtractors. The proposed circuits are designed and simulated using QCA Designer-2.0.3.     

Partial product addition in Vedic design-ripple carry adder design fir filter architecture for electro cardiogram (ECG) signal de-noising application

Design of adder plays a major role in deciding overall performance of system as it is a major building block through generations of design in an innovative design of circuits. In VLSI system and signal processing field applications, various versions of adders are utilized. In applications of signal processing, in recent days, major role is contributed by Finite Impulse Response (FIR) filter. Various authors and papers described its design in a several ways. With the design of effective multiplier, signal denoising application was not explained by any of the existing works. For the generation of partial products, 8-bit multiplier based on a Vedic Mathematics –UrdhvaTiryagbhyam sutra- is proposed in this work. In Vedic multiplier, carry skip method is used for realizing addition of partial product. Four Vedic multipliers of 4 × 4 size are used for designing 8-bit multiplier. Carry skip and UrdhvaTiryagbhyam methods are used for this design. For addition of partial product, this multiplier is designed. Ripple carry adder's logic levels are modified for adding these Vedic multiplier's output. Powerful elimination of ECG noise can be done using this proposed fast FIR filter. In applications of healthcare and biomedical field, they are used. In Vedic design, Ripple Carry Adder (RCA) is used for carrying out partial product addition. Operation of FIR filter with Electro Cardiogram (ECG) signal is done by proposing architecture of FIR filter. It is termed as PPAVD-RCA-FIR and used in de-noising applications. From de-noised signal, Signal to Noise Ratio (SNR), Bit Error Rate (BER) and Mean Square Error (MSE) are computed, which are used for evaluating the performances. When compared with general Vedic multiplier, speed of the proposed design is increased about 13.65% as shown by results.     

基于互补电阻开关的忆阻乘法器设计

现有的忆阻算术逻辑多采用单个忆阻器作为存储单元,在忆阻交叉阵列中易受到漏电流以及设计逻辑电路时逻辑综合复杂度高的影响,导致当前乘法器设计中串行化加法操作的延时和面积开销增加。互补电阻开关具有可重构逻辑电路的运算速度和抑制忆阻交叉阵列中漏电流的性能,是实现忆阻算术逻辑的关键器件。提出一种弱进位依赖的忆阻乘法器。为提升忆阻器的逻辑性能,基于互补电阻开关电路结构,设计两种加法器的优化方案,简化操作步骤。在此基础上,通过改进传统的乘法实现方式,并对进位数据进行拆解,降低运算过程中进位数据之间的依赖性,实现并行化的加法运算。将设计的乘法器映射到混合CMOS/crossbar结构中,乘法计算性能得到大幅提高。在Spice仿真环境下验证所提乘法器的可行性。仿真实验结果表明,与现有的乘法器相比,所提乘法器的延时开销从O(n²)降低为线性级别,同时面积开销降低约70%。     

基于Karatsuba算法低复杂度伽罗华域乘法器设计

提出了一种基于Karatsuba-extended算法的乘法器设计方案,能够更有效地降低[GF(2m)]乘法器的设计复杂度。根据提出的性能参数P,该方案可以设计出最高效的[GF(2m)]乘法器。在m等于2 048的情况下,用该方案设计的乘法器的P约是普通乘法器的3倍。因此,根据实际的不同情况,对于特定m值,该方案通过选择合适的参数r和i,能够设计出最高效的[GF(2m)]乘法器。     

Signed multiplication technique by means of unsigned multiply instruction

The present work aims at proposing an efficient technique for signed binary multiplication using unsigned, multiply instruction. Numerous examples are provided to show efficiency of the proposed approach in the context of practical software implementation. Performance of the technique is compared to the software emulated versions of classical methods, such as radix-2 Booth method, reversal of sign method (negative to positive conversion) and sign extension method. The proposed algorithm is suitable for embedded systems which are based on widespread microprocessors/microcontrollers which have an unsigned multiplication in their instruction set but no signed multiply instruction. The algorithm includes only one unsigned multiplication and two subtractions. Various samples of code presenting the signed multiplication are provided in the assembly language for an MCS-51 compatible microcontroller. The comparison of the performance of algorithm is carried out for classical MCS-51 core and innovative AT89LPx core treated as a reference microcontroller.     

量子可逆逻辑综合的关键技术及其算法

最优化量子可逆逻辑的关键在于用最小的量子代价自动构造量子可逆逻辑.为了提高可逆逻辑自动生成与优化的效率,提出了类模板技术和一种快速算法.模板技术是一个有效的优化工具,类模板技术可以显著提高模板技术的匹配效率;R-M算法是可逆逻辑综合的一种较好的迭代方法,基于R-M算法的原始思想,构造了一个Hash函数,并在此基础上提出了一种可逆逻辑综合的快速算法.实验结果表明,在同等实验环境下使用类模板技术与快速算法,其优化的效果与效率远远优于已知的其他算法.     

Design of reversible logic based full adder in current-mode logic circuits

Demand of Very Large Scale Integration (VLSI) circuits with very high speed and low power are increased due to communication system's transmission speed increase. During computation, heat is dissipated by a traditional binary logic or logic gates. There will be one or more input and only one output in irreversible gates. Input cannot be reconstructed using those outputs. In low power VLSI, reversible logic is commonly preferred in recent days. Information is not lost in reversible gates and back computation is possible in reversible circuits with reduced power dissipation. Reversible full adder circuits are implemented in the previous work to optimize the design and speed of the circuits. Reversible logic gates like TSG, Peres, Feynman, Toffoli, Fredkin are mostly used for designing reversible circuits. However it does not produced a satisfactory result in terms of static power dissipation. In this proposed research work, reversible logic is implemented in the full adder of MOS Current-Mode Logic (MCML) to achieve high speed circuit design with reduced power consumption. In VLSI circuits, reliable performance and high speed operation is exhibited by a MCML when compared with CMOS logic family. Area and better power consumption can be produced implementing reversible logic in full adder of MCML. Minimum garbage output and constant inputs are used in reversible full adder. The experimental results shows that the proposed designed circuit achieves better performance compared with the existing reversible logic circuits such as Feynman gate based FA, Peres gate based FA, TSG based FA in terms of average power, static power dissipation, static current and area.