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An N-bit priority resolver having N inputs and N outputs functions as polling hardware in an embedded system, enabling access to a resource when multiple devices initiate access requests at its inputs which may be located on-chip or off-chip. Subsystems such as data buses, comparators, fixed- and floating-point arithmetic units, interconnection network routers, etc., utilize the priority resolver function. In the literature, there are many transistor-level designs for the priority resolver based on dynamic CMOS logic, some of which are modular and others are not. This article presents a novel gate-level modular design of priority resolvers that can accommodate any number of inputs and outputs. Based on our modular design architecture, small-size priority resolvers can be conveniently combined to form medium- or large-size priority resolvers along with extra logic. The proposed modular design approach helps to reduce the coding complexity compared to the conventional direct design approach and facilitates scalability. We discuss the gate-level implementation of 4-, 8-, 16-, 32-, 64-, and 128-bit priority resolvers based on the direct and modular approaches and provide a performance comparison between these based on the design metrics. According to the modular approach, different sizes of priority resolver modules were used to implement larger-size priority resolvers. For example, a 4-bit priority resolver module was used to implement 8-, 16-, 32-, 64-, and 128-bit priority resolvers in a modular fashion. We used a 28 nm CMOS standard digital cell library and Synopsys EDA tools to synthesize the priority resolvers. The estimated design metrics show that the modular approach tends to facilitate increasing reductions in delay and power-delay product (PDP) compared to the direct approach, especially as the size of the priority resolver increases. For example, a 32-bit modular priority resolver utilizing 16-bit priority resolver modules had a 39.4% reduced delay and a 23.1% reduced PDP compared to a directly implemented 32-bit priority resolver, and a 128-bit modular priority resolver utilizing 16-bit priority resolver modules had a 71.8% reduced delay and a 61.4% reduced PDP compared to a directly implemented 128-bit priority resolver. [ABSTRACT FROM AUTHOR]

Monotonic circuits are a class of input–output mode (IOM) asynchronous circuits that are relaxed compared to quasi-delay-insensitive (QDI) IOM asynchronous circuits in terms of signaling the completion of internal processing. Some recent works have demonstrated the superiority of monotonic logic over QDI logic for arithmetic circuits such as adders and multipliers. This paper presents a new monotonic asynchronous two-bit full adder (TFA) that can be duplicated and cascaded to form a ripple-carry adder (RCA). While an RCA is a slow adder with respect to synchronous design, with respect to IOM asynchronous design an RCA is a noteworthy adder since it has perhaps the least reverse latency that is not attainable through other IOM asynchronous adders. Conventionally, an RCA is constructed via a cascade of one-bit full adders (OFAs). An OFA adds two input bits along with any carry input and produces a sum bit and any carry output. On the other hand, a TFA simultaneously adds two pairs of input bits along with any carry input and produces two sum bits and any carry output. Using our proposed monotonic TFA, we realized an RCA to compare its performance with RCAs constructed using different asynchronous OFAs, and RCAs constructed using existing TFAs. We considered the popular delay-insensitive dual-rail scheme for encoding the adder inputs and outputs, and two 4-phase handshake protocols, namely return-to-zero handshaking (R0H) and return-to-one handshaking (R1H) for communication separately. We used a 28 nm CMOS process for implementation and considered a 32-bit addition as an example. Based on the design metrics estimated, the following inferences were derived: (i) compared to the RCA using the state-of-the-art monotonic OFA, the RCA incorporating the proposed TFA achieved a 26% reduction in cycle time for R0H and a 28.5% reduction in cycle time for R1H while dissipating almost the same power; the cycle time governs the data application rate in an IOM asynchronous circuit, and (ii) compared to the RCA comprising an early output QDI TFA, the RCA incorporating the proposed TFA achieved a 22.3% reduction in cycle time for R0H and a 25.4% reduction in cycle time for R1H while dissipating moderately less power. Also, compared to the existing early output QDI TFA, the proposed TFA occupies 40.9% less area for R0H and 42% less area for R1H. [ABSTRACT FROM AUTHOR]

This article introduces a novel asynchronous full adder that operates in an input–output mode (IOM), displaying both monotonicity and an early output characteristic. In a monotonic asynchronous circuit, the intermediate and primary outputs exhibit similar signal transitions as the primary inputs during data and spacer application. The proposed asynchronous full adder ensures monotonicity for processing data and spacer, utilizing dual-rail encoding for inputs and outputs, and corresponds to return-to-zero (RtZ) and return-to-one (RtO) handshaking. The early output feature of the proposed full adder allows the production of sum and carry outputs based on the adder inputs regardless of the carry input when the spacer is supplied. When utilized in a ripple carry adder (RCA) architecture, the proposed full adder achieves significant reductions in design metrics, such as cycle time, area, and power, compared to existing IOM asynchronous full adders. For a 32-bit RCA implementation using a 28 nm CMOS technology, the proposed full adder outperforms an existing state-of-the-art high-speed asynchronous full adder by reducing the cycle time by 10.4% and the area by 15.8% for RtZ handshaking and reduces the cycle time by 9.8% and the area by 15.8% for RtO handshaking without incurring any power penalty. Further, in terms of the power-cycle time product, which serves as a representative measure of energy, the proposed full adder yields an 11.8% reduction for RtZ handshaking and an 11.2% reduction for RtO handshaking. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The carry look-ahead adder (CLA) is well known among the family of high-speed adders. However, a conventional CLA is not faster than other high-speed adders such as a conditional sum adder (CSA), a carry-select adder (CSLA), and the Kogge–Stone adder (KSA), which is the fastest parallel-prefix adder. Further, in terms of power-delay product (PDP) that characterizes the energy of digital circuits, the conventional CLA is not efficient compared to CSLA and KSA. In this context, this paper presents a high-speed and energy-efficient architecture for the CLA. Many adders ranging from ripple carry to parallel-prefix adders were implemented using a 32-28 nm CMOS standard digital cell library by considering a 32-bit addition. The adders were structurally described in Verilog and synthesized using Synopsys Design Compiler. From the results obtained, it is observed that the proposed CLA achieves a reduction in critical path delay by 55.3% and a reduction in PDP by 45% compared to the conventional CLA. Compared to the CSA, the proposed CLA achieves a reduction in critical path delay by 33.9%, a reduction in power by 26.1%, and a reduction in PDP by 51.1%. Compared to an optimized CSLA, the proposed CLA achieves a reduction in power by 35.4%, a reduction in area by 37.3%, and a reduction in PDP by 37.1% without sacrificing the speed. Although the KSA is faster, the proposed CLA achieves a reduction in power by 39.6%, a reduction in PDP by 6.5%, and a reduction in area by 55.6% in comparison. [ABSTRACT FROM AUTHOR]

This paper analyzes the usefulness of approximate addition for digital image compression. Discrete Cosine Transform (DCT) is an important operation in digital image compression. We used accurate addition and approximate addition individually while calculating the DCT to perform image compression. Accurate addition was performed using the accurate adder and approximate addition was performed using different approximate adders individually. The accurate adder and approximate adders were implemented in an application specific integrated circuit (ASIC)-type design environment using a 32–28 nm complementary metal oxide semiconductor (CMOS) standard cell library and in a field programmable gate array (FPGA)-based design environment using a Xilinx Artix-7 device. Error analysis was performed to calculate the error parameters of various approximate adders by applying one million random input vectors. It is observed that the approximate adders help to better reduce the file size of compressed images than the accurate adder. Simultaneously, the approximate adders enable reductions in design parameters compared to the accurate adder. For an ASIC-type implementation using standard cells, an optimum approximate adder achieved 27.1% reduction in delay, 46.4% reduction in area, and 50.3% reduction in power compared to a high-speed accurate carry look-ahead adder. With respect to an FPGA-based implementation, an optimum approximate adder achieved 8% reduction in delay and 19.7% reduction in power while requiring 47.6% fewer look-up tables (LUTs) and 42.2% fewer flip-flops compared to the native accurate FPGA adder. [ABSTRACT FROM AUTHOR]

Mission- and safety-critical applications tend to incorporate triple modular redundancy (TMR) in their hardware implementation to reliably withstand the fault or failure of any one of the function modules during normal operation, and the function module may be a circuit or a system. In a TMR implementation, two identical copies of a function module are used in addition to the original function module, and the correct operation of at least two function modules is required. In TMR, the corresponding primary outputs of the three function modules are combined using majority voters, which determine the actual primary outputs based on the Boolean majority. Hence, the majority voter is an important component that is useful for conveying the correct operation of a TMR implementation. In the existing literature, many designs of three-input majority voters for TMR have been discussed. However, most of these correspond to the synchronous design style and just one corresponds to the bundled-data asynchronous design style, which is not delay insensitive and hence non-robust. To our knowledge, a robust delay insensitive design of the three-input majority voter has not been considered. In this context, this article presents the designs of robust quasi delay insensitive (QDI) three-input majority voters based on QDI logic synthesis methods, and analyzes which majority voters are preferable in terms of speed, power, and area. We implement example QDI TMR circuits using a QDI full adder as the function module and QDI majority voters using 32/28 nm complementary metal oxide semiconductor (CMOS) technology. The QDI TMR implementations use the delay insensitive dual rail code for data encoding, and four-phase return-to-zero and four-phase return-to-one handshake protocols for data communication. [ABSTRACT FROM AUTHOR]

Given the continuing miniaturization of underlying transistors, electronic functional units (circuits/systems) become increasingly susceptible to high-energy radiation, encountered in applications like space. Hence, redundancy is employed as a radiation hardening by design strategy to cope with faults of functional units used in such applications and to maintain their correct operation. Triple modular redundancy (TMR), which is a subset of N-modular redundancy (NMR), that can mask any single fault or a faulty functional unit has been widely used. However, compared to a simplex implementation a TMR implementation requires two additional functional units and a majority voting logic therefore a TMR implementation's area and power overheads are greater by over 200 %. This is burdensome for resource-constrained applications like space where low power and energy efficiency are important considerations. This paper presents a new redundancy strategy involving approximate computing called RESAC for error-tolerant applications such as digital image/video/audio processing, which is used in space systems. We evaluated the feasibility of RESAC for an image processing case study and the results confirm the usefulness. For implementation using a 28-nm CMOS technology, RESAC achieves reductions in area, delay, and power by 22.3 %, 15.3 %, and 24.9 % compared to TMR. Nonetheless, RESAC can address any NMR. • A novel redundancy scheme utilizing approximate computing called RESAC is proposed. • RESAC is suitable for use in inherently error-tolerant applications like digital signal processing. • A comparison between TMR and RESAC is performed for a digital image processing application. • RESAC produces images of good quality comparable to those produced by TMR. • For implementation, RESAC achieves 22.3 % reduced area, 15.3 % reduced delay, and 24.9 % reduced power compared to TMR. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper presents a new, efficient asynchronous early output majority voter that can be used to effectively realize an asynchronous triple modular redundancy (TMR) implementation. For the input-output mode asynchronous realization, the dual-rail code was used for data encoding and four phase return-to-zero and return-to-one handshake schemes were separately used for data communication. The proposed majority voter requires 62.8% less area and dissipates 37% less power on average compared to the best of the existing asynchronous majority voters while considering both handshake schemes. Importantly, the reductions in area and power are achieved without sacrificing the speed. Example TMR implementations show that the proposed majority voter leads to simultaneous reductions in cycle time, silicon area, and power dissipation. As a result, the proposed majority voter enables improved optimization in figure-of-merits such as area–cycle time product, power–cycle time product, and area–cycle time–power product for TMR implementations utilizing it compared to TMR implementations incorporating other majority voters. The circuits were implemented using a 32/28-nm CMOS technology. [ABSTRACT FROM AUTHOR]

This article describes the design of approximate array multipliers by making vertical or horizontal cuts in an accurate array multiplier followed by different input and output assignments within the multiplier. We consider a digital image denoising application and show how different combinations of input and output assignments in an approximate array multiplier affect the quality of the denoised images. We consider the accurate array multiplier and several approximate array multipliers for synthesis. The multipliers were described in Verilog hardware description language and synthesized by Synopsys Design Compiler using a 32/28-nm complementary metal-oxide-semiconductor technology. The results show that compared to the accurate array multiplier, one of the proposed approximate array multipliers viz. PAAM01-V7 achieves a 28% reduction in critical path delay, 75.8% reduction in power, and 64.6% reduction in area while enabling the production of a denoised image that is comparable in quality to the image denoised using the accurate array multiplier. The standard design metrics such as critical path delay, total power dissipation, and area of the accurate and approximate multipliers are given, the error parameters of the approximate array multipliers are provided, and the original image, the noisy image, and the denoised images are also depicted for comparison. [ABSTRACT FROM AUTHOR]