Novel designs for fault tolerant reversible binary coded decimal adders

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.     

四量子可逆逻辑电路快速综合算法

量子可逆逻辑电路综合是以较小量子代价自动构造所求量子可逆逻辑电路.本文提出了一种新颖高效的4量子电路综合算法,巧妙构造置换的最短编码,通过对量子电路进行特定拓扑变换,无损压缩n量子最优电路占用内存空间近2×n!倍,通过对已生成最优电路的双向级联,可使用多种量子门,采用最小长度标准,以极高效率生成较长的4量子电路,如率先生成基于控制非门、非门、Toffoli门库的全部前8层共3120218828个电路,还可快速综合任意长度不超过16的最优电路,并对4量子标准测试电路进行快速且全面的优化.     

基于遗传算法的量子可逆逻辑电路综合方法研究

量子可逆逻辑电路综合主要是研究在给定的量子门和量子电路的约束条件及限制下,找到最小或较小的量子代价实现所需量子逻辑功能的电路。把量子逻辑门的功能用矩阵的数学模型表示,用遗传算法作全局搜索工具,将遗传算法应用于量子可逆逻辑电路综合,是一种全新的可逆逻辑电路综合方法,实现了合成、优化同步进行。四阶量子电路实验已取得了很好的效果,并进一步分析了此方法在高阶量子电路综合问题上的应用前景。     

Designing novel reversible BCD adder and parallel adder/subtraction using new reversible logic gates

Reversible logic has received much attention in recent years when calculation with minimum energy consumption is considered. Especially, interest is sparked in reversible logic by its applications in some technologies, such as quantum computing, low-power CMOS design, optical information processing and nanotechnology. This article proposes two new reversible logic gates, ZRQ and NC. The first gate ZRQ not only implements all Boolean functions but also can be used to design optimised adder/subtraction architectures. One of the prominent functionalities of the proposed ZRQ gate is that it can work by itself as a reversible full adder/subtraction unit. The second gate NC can complete overflow detection logic of Binary Coded Decimal (BCD) adder. This article proposes two approaches to design novel reversible BCD adder using new reversible gates. A comparative result which is presented shows that the proposed designs are more optimised in terms of number of gates, garbage outputs, quantum costs and unit delays than the existing designs.     

An Exact approach for Complete Test Set Generation of Toffoli-Fredkin-Peres based Reversible Circuits

Reversible logic has gained interest of researchers worldwide for its ultra-low power and high speed computing abilities in the future quantum information processing. Testing of these circuits is important for ensuring high reliability of their operation. In this work, we propose an ATPG algorithm for reversible circuits using an exact approach to generate CTS (Complete Test Set) which can detect single stuck-at faults, multiple stuck-at faults, repeated gate fault, partial and complete missing gate faults which are very useful logical fault models for reversible logic to model any physical defect. Proposed algorithm can be used to test a reversible circuit designed with k-CNOT, Peres and Fredkin gates. Through extensive experiments, we have validated our proposed algorithm for several benchmark circuits and other circuits with family of reversible gates. This algorithm produces a minimal and complete test set while reducing test generation time as compared to existing state-of-the-art algorithms. A testing tool is developed satisfying the purpose of generating all possible CTS’s indicating the simulation time, number of levels and gates in the circuit. This paper also contributes to the detection and removal of redundant faults for optimal test set generation.     

Transistor realization of reversible “ZS” series gates and reversible array multiplier

In order to reduce the redundant Toffoli gates and the line-crossings in the classical reversible full adder appearing in the present literatures, this paper gives a reconstructive structure of Fredkin gate, called RF gate, the corresponding quantum equivalent realization and electronic circuitry construction based on CMOS technology and pass-transistor of this gate are also designed in this paper. With the assistance of the RF gate and the basic reversible gates (including NOT gate, CNOT gate and Toffoli gate), we design new 4×4 reversible gates called “ZS” series gates and its corresponding electronic circuitry construction. The proposed “ZS” series gates have the ability to operate reversible add operation between two signed numbers by a single gate and at lower power consumption. At the same time, as an application of “ZS” series gates, this paper also designs reversible array multiplier in order to achieve the signed multiplication. It can be theoretically proved that the proposed reversible array multiplier can eliminate power loss associated with the irreversible operation of classical computer, and will be exponentially lower than reversible parallel multiplier with respect to time complexity.     

非可逆逻辑门的量子可逆实现研究

逻辑关系可用逻辑函数表示,量子逻辑关系是可逆的,引入和定义了量子逻辑函数;通过引入辅助量子位,增添量子输出信号的区分位,完成对非可逆逻辑门的改造,使非可逆逻辑门在量子电路中得到可逆实现,并研究了一些有用的非可逆逻辑门的改造方法,给出可实现的优化后的量子电路。     

Power consumption estimation in CMOS VLSI chips

Power consumption from logic circuits, interconnections, clock distribution, on chip memories, and off chip driving in CMOS VLSI is estimated. Estimation methods are demonstrated and verified. An estimate tool is created. Power consumption distribution between interconnections, clock distribution, logic gates, memories, and off chip driving are analyzed by examples. Comparisons are done between cell library, gate array, and full custom design. Also comparisons between static and dynamic logic are given. Results show that the power consumption of all interconnections and off chip driving can be up to 20% and 65% of the total power consumption respectively. Compared to cell library design, gate array designed chips consume about 10% more power, and power reduction in full custom designed chips could be 15%     

Exact synthesis of three-qubit quantum circuits from non-binary quantum gates

Because of recent nano-technological advances, nano-structured systems have become highly ordered, making it quantum computing schemas possible. We propose an approach to optimally synthesise quantum circuits from non-permutative quantum gates such as controlled-square-root-of-not (i.e., controlled-V). Our approach reduces the synthesis problem to multiple-valued optimisation and uses group theory. We devise a novel technique that transforms the quantum logic synthesis problem from a multi-valued constrained optimisation problem to a permutable representation. The transformation enables us to use group theory to exploit the symmetric properties of the synthesis problem. Assuming a cost of one for each two-qubit gate, we found all reversible circuits with quantum costs of 4, 5, 6, etc., and give another algorithm to realise these reversible circuits with quantum gates. The approach can be used for both binary permutative deterministic circuits and probabilistic circuits such as controlled random-number generators and hidden Markov models.     

基于矩阵编码的量子可逆逻辑电路进化设计方法

 本文研究基于遗传算法的量子可逆逻辑电路综合技术,能实现可逆逻辑电路功能、量子门数、垃圾位数和量子代价的多目标优化设计.建立了量子可逆逻辑电路综合数学模型,采用了量子可逆逻辑电路矩阵编码方案,设计了量子可逆逻辑电路进化操作算子,给出了量子可逆逻辑电路多目标进化设计算法.以8位量子可逆乘法器为设计实例,实验结果证明了所提出的量子可逆逻辑电路多目标进化设计方法是正确有效的.     

Efficient reversible NOR gates and their mapping in optical computing domain

Reversible logic is a computing paradigm in which there is a one to one mapping between the input and the output vectors. Reversible logic gates are implemented in an optical domain as it provides high speed and low energy computations. In the existing literature there are two types of optical mapping of reversible logic gates: (i) based on a semiconductor optical amplifier (SOA) using a Mach–Zehnder interferometer (MZI) switch; (ii) based on linear optical quantum computation (LOQC) using linear optical quantum logic gates. In reversible computing, the NAND logic based reversible gates and design methodologies based on them are widely popular. The NOR logic based reversible gates and design methodologies based on them are still unexplored. In this work, we propose two NOR logic based n-input and n-output reversible gates one of which can be efficiently mapped in optical computing using the Mach–Zehnder interferometer (MZI) while the other one can be mapped efficiently in optical computing using the linear optical quantum gates. The proposed reversible NOR gates work as a corresponding NOR counterpart of NAND logic based Toffoli gates. The proposed optical reversible NOR logic gates can implement the reversible boolean logic functions with a reduced number of linear optical quantum logic gates or reduced optical cost and propagation delay compared to their implementation using existing optical reversible NAND gates. It is illustrated that an optical reversible gate library having both optical Toffoli gate and the proposed optical reversible NOR gate is superior compared to the library containing only the optical Toffoli gate: (i) in terms of number of linear optical quantum gates when implemented using linear optical quantum computing (LOQC), (ii) in terms of optical cost and delay when implemented using the Mach–Zehnder interferometer.     

基于Q-M算法的量子可逆逻辑电路综合方法

提出了合并(化简)规则,并按合并规则修改了Q-M算法源码,获得积之异或和表达式,成功地实现了将不可逆操作转换为可逆操作。该规则应用于常规逻辑综合的Q-M算法移植到可逆逻辑综合中,以便利用可逆逻辑门来构造可逆逻辑电路。     

一种容错可逆的通用移位寄存器设计

为了使计算系统具有低功耗和容错能力,基于可逆逻辑设计了一种容错的通用移位寄存器。提出了一种新型的容错可逆逻辑门(Parity-Preserving D Flip_flop Gate, PP_DFG),利用它和存在的容错门,完成了寄存器和多路数据选择器的设计。综合上述模块,构建了容错可逆的通用移位寄存器电路,用Verilog 硬件描述语言建模,仿真显示电路逻辑结构正确。同现有电路相比,根据量子代价、延迟和无用输出对其进行性能评估,结果表明该电路不仅具有容错功能,而且性能提高了16%~50%。设计的电路可作为一种重要的存储元件应用于未来的低功耗计算系统。     

Sleep switch dual threshold voltage domino logic with reduced subthreshold and gate oxide leakage current

A circuit technique is proposed in this paper for simultaneously reducing the subthreshold and gate oxide leakage power consumption in domino logic circuits. PMOS-only sleep transistors and a dual threshold voltage CMOS technology are utilized to place an idle domino logic circuit into a low leakage state. Sleep transistors are added to the dynamic nodes in order to reduce the subthreshold leakage current by strongly turning off all of the high threshold voltage transistors. Similarly, the sleep switches added to the output nodes suppress the voltages across the gate insulating layers of the transistors in the fan-out gates, thereby minimizing the gate tunneling current. The proposed circuit technique lowers the total leakage power by 88 to 97% as compared to the standard dual threshold voltage domino logic circuits. Similarly, a 22 to 44% reduction in the total leakage power is observed as compared to a previously published sleep switch scheme in a 45 nm CMOS technology.     

基于NCV门库的可逆逻辑门进化设计与优化

提出和实现了一种基于遗传算法的可逆逻辑门的设计方法。其特点是预先求出并存储所需功能的可逆逻辑门的真值表,并对NCV基本门库中的控制V门,控制V+门,控制非门,非门进行编码,通过这些基本门的级联,构成染色体暨可逆逻辑门,在逐代进化中按照既定逻辑功能和优化目标进行适应度评估,再利用遗传换代中的选择,交叉,变异等功能进行遗传操作,进而找到功能和性能均符合预定目标的可逆逻辑门。实验结果证明,此方法的可行性、有效性,与传统手工设计可逆逻辑门相比,其在求解速度和能力方面有显著提高。     

PMOS-Only Sleep Switch Dual-Threshold Voltage Domino Logic in Sub-65-nm CMOS Technologies

A circuit technique is proposed in this paper for simultaneously reducing the subthreshold and gate oxide leakage power consumption in domino logic circuits. Only p-channel sleep transistors and a dual-threshold voltage CMOS technology are utilized to place an idle domino logic circuit into a low leakage state. Sleep transistors are added to the dynamic nodes in order to reduce the subthreshold leakage current by strongly turning off all of the high-threshold voltage transistors. Similarly, the sleep switches added to the output nodes suppress the voltages across the gate insulating layers of the transistors in the fan-out gates, thereby minimizing the gate tunneling current. The proposed circuit technique lowers the total leakage power by up to 77% and 97% as compared to the standard dual-threshold voltage domino logic circuits at the high and low die temperatures, respectively. Similarly, a 22% to 44% reduction in the total leakage power is observed as compared to a previously published sleep switch scheme in a 45-nm CMOS technology. The energy overhead of the circuit technique is low, justifying the activation of the proposed sleep scheme by providing a net savings in total energy consumption during short idle periods.     

A Kernel‐Based Partitioning Algorithm for Low‐Power,Low‐Area Overhead Circuit Design Using Don't‐Care Sets

This letter proposes an efficient kernel‐based partitioning algorithm for reducing area and power dissipation in combinational circuit designs using don't‐care sets. The proposed algorithm decreases power dissipation by partitioning a given circuit using a kernel extracted from the logic. The proposed algorithm also reduces the area overhead by minimizing duplicated gates in the partitioned sub‐circuits. The partitioned subcircuits are further optimized utilizing observability don't‐care sets. Experimental results for the MCNC benchmarks show that the proposed algorithm synthesizes circuits that on the average consume 22.5% less power and have 12.7% less area than circuits generated by previous algorithms based on a precomputation scheme.     

High-Throughput Area-Efficient Processor for Cryptography

Cryptography circuits for portable elec-tronic devices provide user authentication and secure data communication. These circuits should, achieve high per-formance, occupy small chip area, and handle several cryptographic algorithms. This paper proposes a high-performance ASIP (Application specific instruction set processor) for five standard cryptographic algorithms in-cluding both block ciphers (AES, Camellia, and ARIA) and stream ciphers (ZUC and SNOW 3G). The processor reaches ASIC-like performance such as 11.6 Gb/s for AES encryption, 16.0 Gb/s for ZUC, and 32.0 Gb/s for SNOW 3G, etc under the clock frequency of 1.0 GHz with the area consumption of 0.56 mm2 (65 nm). Compared with state-of-the-art VLSI designs, our design achieves high perfor-mance, low silicon cost, low power consumption, and suf-ficient programmability. For its programmability, our de-sign can offer algorithm modification when an algorithm supported is unfortunately cracked and invalid to use. The product lifetime of our design can thus be extended.     

可逆逻辑门进化设计方法的CUDA实现

可逆逻辑门优化程度将直接影响可逆逻辑电路的整体优化,目前已有的优化方法难以实现全局最优。文中基于NCV门库,对遗传算法编码方案和适应度进行了改进,并将进化设计方法改造为CUDA架构下的并行算法应用到可逆逻辑门的优化。其不仅发挥了电路进化设计的全局优化能力,且在不增加硬件规模的前提下,明显提高了电路的搜索速度。     

基于新型量子逻辑门库的最优NCV三量子电路快速综合算法

许多量子电路综合算法由于指数级时间与空间复杂度,只能用可逆逻辑门综合3量子逻辑电路,仅有少数算法实现用量子非门,控制非门,控制V门与控制V⁺门(NCV)综合3量子逻辑电路,主要方法是将电路综合问题简化为四值逻辑综合问题.本文提出用NCV门构造新型量子逻辑门库,该库与NCV门库在综合最优3量子逻辑电路上等价,因此又可将四值逻辑综合问题进一步简化为更易求解的二值逻辑综合问题,使用基于完备Hash函数的3量子电路快速综合算法,快速生成全部最优的3量子逻辑电路,以最小代价综合电路的平均速度是目前最好结果Maslov 2007的近127倍.