Asynchronous quasi-delay-insensitive (QDI) implementation of approximate addition is described in this article. The objective is to provide an insight into the optimization in design metrics that can be achieved with approximate addition compared to accurate addition based on a QDI implementation by considering a practical digital image processing application. For the QDI implementation, some approximate adder architectures are considered which are deemed suitable for both ASIC and FPGA based implementations. The accurate and approximate adders considered are of size 32-bits. The delay-insensitive dual-rail code was used for data encoding, and four-phase return-to-zero (RTZ) and return-to-one (RTO) handshake protocols were used separately for data communication. The implementations used a 32/28-nm complementary metal oxide semiconductor (CMOS) technology. The simulation results show that an approximate adder HOERAA achieves a 19.7% reduction in cycle time, a 12.5% reduction in area, and an 17.7% reduction in energy compared to the accurate adder for RTZ handshaking. For RTO handshaking, HOERAA achieves an 18.7% reduction in cycle time, a 12.4% reduction in area, and a 16.6% reduction in energy compared to the accurate adder. Another approximate adder HEAA achieves a 19.7% reduction in cycle time, a 12.9% reduction in area, and a 20.2% reduction in energy, compared to the accurate adder for RTZ handshaking. For RTO handshaking, HEAA achieves an 18.7% reduction in cycle time, a 12.9% reduction in area, and a 19.2% reduction in energy compared to the accurate adder. Nevertheless, the RTO handshaking is preferable to RTZ handshaking as the former facilitates slightly better optimizations in design metrics compared to the latter. The mean absolute error (MAE) and the root mean square error (RMSE), which are popular error metrics used in approximate computing, were calculated for the approximate adders and are given for a comparison. While the MAE of HOERAA and HEAA are comparable, HOERAA has 8.6% reduced RMSE compared to HEAA. Digital image processing results based on accurate and approximate additions are also given, to substantiate the usefulness of approximate addition.
A new algorithm called Character-Comparison to Character-Access (CCCA) is developed to test the effect of both: 1) converting character-comparison and number-comparison into character-access and 2) the starting point of checking on the performance of the checking operation in string searching. An experiment is performed; the results are compared with five algorithms, namely, Naive, BM, Inf_Suf_Pref, Raita, and Circle. With the CCCA algorithm, the results suggest that the evaluation criteria of the average number of comparisons are improved up to 74.0%. Furthermore, the results suggest that the clock time required by the other algorithms is improved in range from 28% to 68% by the new CCCA algorithm
This paper deals with a power-conscious ANDEXOR- Inverter type logic implementation for a complex class of Boolean functions, namely Achilles- heel functions. Different variants of the above function class have been considered viz. positive, negative and pure horn for analysis and simulation purposes. The proposed realization is compared with the decomposed implementation corresponding to an existing standard AND-EXOR logic minimizer; both result in Boolean networks with good testability attribute. It could be noted that an AND-OR-EXOR type logic network does not exist for the positive phase of this unique class of logic function. Experimental results report significant savings in all the power consumption components for designs based on standard cells pertaining to a 130nm UMC CMOS process The simulations have been extended to validate the savings across all three library corners (typical, best and worst case specifications).
GDI (gate diffusion input) based technique for low power combinational logic circuit design has been elaborately discussed and the advantage of this design style over static CMOS (SC) implementation and pass-transistor logic (PTL), with regard to power consumption, delay and area complexity is also described in recent literature (Morgenshtein, 2002). In this paper, we propose a couple of new GDI based cell designs, which are found to be much more power efficient in comparison with existing GDI based cell functionality. The significance of these designs is substantiated by the simulation results obtained for a 0.35 muM TSMC CMOS technology, where an improvement in power efficiency of the order of 2-3times is reported in the pre-layout stage for some widely used important digital arithmetic circuits
Error resiliency, which signifies the capability of a circuit to tolerate errors and produce correct outputs, assumes greater significance for digital design in the nanoscale regime due to the relentless miniaturization of semiconductor devices. In this context, the self-timed design paradigm forms an attractive and viable alternative for the VLSI design community. In this paper, the error resiliency of a predominantly used asynchronous logic primitive viz. The Muller C-element is estimated and compared alongside the error resiliencies of combinational logic primitives. The probabilistic analysis reveals that the Muller C-element has good error tolerance similar to that of AND, NAND, OR and NOR gates, and features superior error immunity compared to XOR and XNOR gate types.
This paper makes a comparison between various quasi-delay-insensitive (QDI) asynchronous ripple carry adders (RCAs) realized using a delay-insensitive dual-rail code which correspond to 4-phase return-to-zero (RTZ) and 4-phase return-to-one (RTO) handshaking. The QDI RCAs considered are 32-bits in size and correspond to a variety of timing regimes viz. strong-indication, weak-indication, early output, and relative-timed, which are implemented using a 32/28nm CMOS process. The extensive comparisons show that, overall, QDI RCAs which correspond to the RTO protocol are optimized compared to their QDI RCA counterparts which correspond to the RTZ protocol in terms of area, power dissipation, latency, and cycle time.
This article presents two area/latency optimized gate level asynchronous full adder designs which correspond to early output logic. The proposed full adders are constructed using the delay-insensitive dual-rail code and adhere to the four-phase return-to-zero handshaking. For an asynchronous ripple carry adder (RCA) constructed using the proposed early output full adders, the relative-timing assumption becomes necessary and the inherent advantages of the relative-timed RCA are: (1) computation with valid inputs, i.e., forward latency is data-dependent, and (2) computation with spacer inputs involves a bare minimum constant reverse latency of just one full adder delay, thus resulting in the optimal cycle time. With respect to different 32-bit RCA implementations, and in comparison with the optimized strong-indication, weak-indication, and early output full adder designs, one of the proposed early output full adders achieves respective reductions in latency by 67.8, 12.3 and 6.1 %, while the other proposed early output full adder achieves corresponding reductions in area by 32.6, 24.6 and 6.9 %, with practically no power penalty. Further, the proposed early output full adders based asynchronous RCAs enable minimum reductions in cycle time by 83.4, 15, and 8.8 % when considering carry-propagation over the entire RCA width of 32-bits, and maximum reductions in cycle time by 97.5, 27.4, and 22.4 % for the consideration of a typical carry chain length of 4 full adder stages, when compared to the least of the cycle time estimates of various strong-indication, weak-indication, and early output asynchronous RCAs of similar size. All the asynchronous full adders and RCAs were realized using standard cells in a semi-custom design fashion based on a 32/28 nm CMOS process technology.
India is marching towards achieving a desirable status of a developed country with rapid strides. Ensuring uninterrupted supply of energy to support economic and commercial activities is essential for sustainable economic growth. In true sense, sustainable development should be widely spread in all three dimensions - social, economic, and environmental. For all these areas, energy is perhaps the most important aspect. The production and the consumption patterns at the local and the global scale, determine not only all the activities in society, but also some major environmental issues like pollution, green house effect, and desertification. This paper presents the scenario of power generation, consumption and forecasts power requirements up to 13th five year plan. While it also stressing on energy and its close linkages with environment, poverty and sustainability. This also describes the strategies to meet the necessary demand of power and steps taken to achieve sustainability.
Multiplication is a widely used arithmetic operation in microprocessing and digital signal processing applications, and multiplication is realized using a multiplier. This article presents the quasi-delay-insensitive (QDI) early output versions of recently reported indicating asynchronous array multipliers. Delay-insensitive dual-rail encoding is used for data representation and processing, and 4-phase return-to-zero (RTZ) and return-to-one (RTO) handshake protocols are used for data communication. Many QDI array multipliers were realized using a 32/28 nm complementary metal oxide semiconductor (CMOS) technology. Compared to the optimum indicating array multiplier, the proposed optimum early output array multiplier achieves a 6.2% reduction in cycle time and a 7.4% reduction in power-cycle time product (PCTP) with respect to RTZ handshaking, and a 7.6% reduction in cycle time and an 8.8% reduction in PCTP with respect to RTO handshaking without an increase in the area. The simulation results also convey that the RTO handshaking is preferable to the RTZ handshaking for the optimum implementation of QDI array multipliers.
We present a novel fast bipartitioned hybrid adder (FBHA) that utilizes carry-select and carry-lookahead logic. The proposed FBHA is an accurate adder with a significant part and a less significant part joined together by a carry signal. In an N-bit FBHA, the K-bit less significant part is realized using carry-lookahead adder logic, and the (N-K)-bit significant part is realized using carry-select adder logic. The 32-bit addition was considered as an example operation for this work. Many 32-bit adders ranging from the slow ripple carry adder to the fast parallel-prefix Kogge-Stone adder and the proposed adder were synthesized using a 28-nm CMOS standard cell library and their design metrics were compared. A well-optimized FBHA achieved significant optimizations in design metrics compared to its high-speed adder counterparts and some examples are mentioned as follows: (a) 19.8% reduction in delay compared to a carry-lookahead adder; (b) 19.8% reduction in delay, 24.4% reduction in area, and 19.4% reduction in power compared to a carry-select adder; (c) 45.6% reduction in delay, and 13.5% reduction in power compared to a conditional sum adder; and (d) 46.5% reduction in area, and 29.3% reduction in power compared to the Kogge-Stone adder.
Digital image blending is commonly used in applications such as photo editing and computer graphics where two images are combined to produce a desired blended image. Digital images can be blended by addition or multiplication, and usually exact addition or multiplication is performed for image blending. In this paper, we evaluate the usefulness of inexact multiplication for digital image blending. Towards this, we describe how an exact array multiplier can be made inexact by introducing vertical cut(s) in it and assigning distinct combinations of binary values to the dangling inputs and product bits. We considered many 8-bit digital images for blending and the blended images obtained using exact and inexact multipliers are shown, which demonstrates the usefulness of inexact multiplication for image blending. For 8 × 8 image blending, one of our inexact array multipliers viz. IAM01-VC8 was found to achieve 63.3% reduction in area, 21% reduction in critical path delay, 72.3% reduction in power dissipation, and 78.1% reduction in energy compared to the exact array multiplier. In addition, IAM01-VC8 achieved 60.6% reduction in area, 9.7% reduction in critical path delay, 64.7% reduction in power dissipation, and 68.1% reduction in energy compared to the high-speed exact 8 × 8 multiplier that was automatically synthesized using a logic synthesis tool. The exact and inexact multipliers were physically realized using 32/28 nm CMOS process technology.
Approximate or inaccurate addition is found to be viable for practical applications which have an inherent error tolerance. Approximate addition is realized using an approximate adder, and many approximate adder designs have been put forward in the literature targeting an acceptable trade-off between quality of results and savings in design metrics compared to the accurate adder. Approximate adders can be classified into three categories as: (a) suitable for FPGA implementation, (b) suitable for ASIC type implementation, and (c) suitable for FPGA and ASIC type implementations. Among these, approximate adders, which are suitable for FPGA and ASIC type implementations are particularly interesting given their versatility and they are typically designed at the gate level. Depending on the way approximation is built into an approximate adder, approximate adders can be classified into two kinds as static approximate adders and dynamic approximate adders. This paper compares and analyzes static approximate adders which are suitable for both FPGA and ASIC type implementations. We consider many static approximate adders and evaluate their performance for a digital image processing application using standard figures of merit such as peak signal to noise ratio and structural similarity index metric. We provide the error metrics of approximate adders, and the design metrics of accurate and approximate adders corresponding to FPGA and ASIC type implementations. For the FPGA implementation, we considered a Xilinx Artix-7 FPGA, and for an ASIC type implementation, we considered a 32/28 nm CMOS standard digital cell library. While the inferences from this work could serve as a useful reference to determine an optimum static approximate adder for a practical application, in particular, we found approximate adders HOAANED, HERLOA and M-HERLOA to be preferable.
Approximate ripple carry adders (RCAs) and carry lookahead adders (CLAs) are presented which are compared with accurate RCAs and CLAs for performing a 32-bit addition. The accurate and approximate RCAs and CLAs are implemented using a 32/28nm CMOS process. Approximations ranging from 4- to 20-bits are considered for the less significant adder bit positions. The simulation results show that approximate RCAs report reductions in the power-delay product (PDP) ranging from 19.5% to 82% than the accurate RCA for approximation sizes varying from 4- to 20-bits. Also, approximate CLAs report reductions in PDP ranging from 16.7% to 74.2% than the accurate CLA for approximation sizes varying from 4- to 20-bits. On average, for the approximation sizes considered, it is observed that approximate CLAs achieve a 46.5% reduction in PDP compared to the approximate RCAs. Hence, approximate CLAs are preferable over approximate RCAs for the low power implementation of approximate computer arithmetic.
We present a novel fast bipartitioned hybrid adder (FBHA) that utilizes carry-select and carry-lookahead logic. The proposed FBHA is an accurate adder with a si
For digital system designs, triple modular redundancy (TMR), which is a 3-tuple version of N-modular redundancy is widely preferred for many mission-control and safety-critical applications. The TMR scheme involves two-times duplication of the simplex system hardware, with a majority voter ensuring correctness provided at least two out of three copies of the system remain operational. Thus the majority voter plays a pivotal role in ensuring the correct operation of the system. The fundamental assumption implicit in the TMR scheme is that the majority voter does not become faulty, which may not hold well for implementations based on latest technology nodes with dimensions of the order of just tens of nanometers. To overcome the drawbacks of the classical majority voter some new voter designs were put forward in the literature with the aim of enhancing the fault tolerance. However, these voter designs generally ensure the correct system operation in the presence of either a faulty function module or the faulty voter, considered only in isolation. Since multiple faults may no longer be excluded in the nanoelectronics regime, simultaneous fault occurrences on both the function module and the voter should be considered, and the fault tolerance of the voters have to be analyzed under such a scenario. In this context, this article proposes a new fault-tolerant majority voter which is found to be more robust to faults than the existing voters in the presence of faults occurring internally and/or externally to the voter. Moreover, the proposed voter features less power dissipation, delay, and area metrics based on the simulation results obtained by using a 32/28nm CMOS process.
No abstract is provided for this article.
Cyclic symmetric structures such as centrifugal fan impellers are considered in this paper. One of the identical sectors is chosen for the finite element analysis. A triangular plate element is employed. The stiffness and load matrices are obtained in cylindrical coordinates. The displacements are obtained using a modified submatrices elimination scheme. The efficiency of this scheme is discussed. Impeller stresses are calculated and checked with the results obtained using a strain gauge technique.
We present a new asynchronous quasi-delay-insensitive (QDI) block carry lookahead adder with redundant carry (BCLARC) realized using delay-insensitive dual-rail data encoding and 4-phase return-to-zero (RTZ) and 4-phase return-to-one (RTO) handshaking. The proposed QDI BCLARC is found to be faster and energy-efficient than the existing asynchronous adders which are QDI and non-QDI (i.e., relative-timed). Compared to existing asynchronous adders corresponding to various architectures such as the ripple carry adder (RCA), the conventional carry lookahead adder (CCLA), the carry select adder (CSLA), the BCLARC, and the hybrid BCLARC-RCA, the proposed BCLARC is found to be faster and more energy-optimized. The cycle time (CT), which is expressed as the sum of the worst-case times taken for processing the data and the spacer, governs the speed. The product of average power dissipation and CT viz. the power-cycle time product (PCTP) defines the low power/energy efficiency. For a 32-bit addition, the proposed QDI BCLARC achieves the following reductions in design metrics on average over its counterparts when considering RTZ and RTO handshaking: i) 20.5% and 19.6% reductions in CT and PCTP respectively compared to an optimum QDI early output RCA, ii) 16.5% and 15.8% reductions in CT and PCTP respectively compared to an optimum relative-timed RCA, iii) 32.9% and 35.9% reductions in CT and PCTP respectively compared to an optimum uniform input-partitioned QDI early output CSLA, iv) 47.5% and 47.2% reductions in CT and PCTP respectively compared to an optimum QDI early output CCLA, v) 14.2% and 27.3% reductions in CT and PCTP respectively compared to an optimum QDI early output BCLARC, and vi) 12.2% and 11.6% reductions in CT and PCTP respectively compared to an optimum QDI early output hybrid BCLARC-RCA. The adders were implemented using a 32/28nm CMOS technology.
