Approximate Compressors for Multiplication

At nanometric scales, approximate computing is an attractive prototype used for digital processing. Despite providing less accurate results, approximate computing is preferred over exact computing as it provides a fast & significant output along with low power consumption. Designing of an efficient multiplier has always been a challenge for VLSI designers as multipliers have a large area, long latency consumes considerable power. For this inconvenience compressor with low latency, low power consumption and reduced stages of the product are designed. This paper proposes two methods to design high order compressors (8:4 & 9:4) (i) Using adders (half & full) (ii) Using multiplexers in Cadence VIRTUOSO tool using 45nm technology. Extensive simulation results show that the proposed designs achieve significant accuracy improvement along with power, area, and delay reductions compared to previous compressor designs

High performance 8-bit approximate multiplier using novel 4:2 approximate compressors for fast image processing

In this paper, a novel 8-bit approximate multiplier is proposed based on three novel 4:2 approximate compressors which its delay and error is less than those of the multipliers constructed by traditional 4:2 approximate compressors, and its delay is also less than that of an 8-bit multiplier constructed by using 3:2 precise compressors. To do so, each novel compressor is designed such that its output carry is independent of the output carry of its previous compressor in the multiplier. Therefore, the problem of carry propagation delay is eliminated and a fast multiplier is constructed. To obtain the most accurate multiplier, the best compressor of the three proposed compressors for each multiplier’s column is determined using the genetic algorithm. Moreover, one can use the approximate compressors only at the k least significant multiplier’s columns for more error reduction. The proposed multiplier is used for image blending and image compression. Our simulations show that for example the error and the delay of the proposed method for k=9 is at-least 32.52% and 33.10% less than those of traditional 4:2 approximate compressor based multipliers, respectively.Abstract: In this paper, a novel 8-bit approximate multiplier is proposed based on three novel 4:2 approximate compressors which its delay and error is less than those of the multipliers constructed by traditional 4:2 approximate compressors, and its delay is also less than that of an 8-bit multiplier constructed by using 3:2 precise compressors. To do so, each novel compressor is designed such that its output carry is independent of the output carry of its previous compressor in the multiplier. Therefore, the problem of carry propagation delay is eliminated and a fast multiplier is constructed. To obtain the most accurate multiplier, the best compressor of the three proposed compressors for each multiplier’s column is determined using the genetic algorithm. Moreover, one can use the approximate compressors only at the k least significant multiplier’s columns for more error reduction. The proposed multiplier is used for image blending and image compression. Our simulations show that for example the error and the delay of the proposed method for k=9 is at-least 32.52% and 33.10% less than those of traditional 4:2 approximate compressor based multipliers, respectively

A Reconfigurable Digital Multiplier and 4:2 Compressor Cells Design

With the continually growing use of portable computing devices and increasingly complex software applications, there is a constant push for low power high speed circuitry to support this technology. Because of the high usage and large complex circuitry required to carry out arithmetic operations used in applications such as digital signal processing, there has been a great focus on increasing the efficiency of computer arithmetic circuitry. A key player in the realm of computer arithmetic is the digital multiplier and because of its size and power consumption, it has moved to the forefront of today\u27s research. A digital reconfigurable multiplier architecture will be introduced. Regulated by a 2-bit control signal, the multiplier is capable of double and single precision multiplication, as well as fault tolerant and dual throughput single precision execution. The architecture proposed in this thesis is centered on a recursive multiplication algorithm, where a large multiplication is carried out using recursions of simpler submultiplier modules. Within each sub-multiplier module, instead of carry save adder arrays, 4:2 compressor rows are utilized for partial product reduction, which present greater efficiency, thus result in lower delay and power consumption of the whole multiplier. In addition, a study of various digital logic circuit styles are initially presented, and then three different designs of 4:2 compressor in Domino Logic are presented and simulation results confirm the property of proposed design in terms of delay, power consumption and operation frequenc

Design and Implementation of Hybrid Multiplier for DSP Applications

In recent decades, there has been a consistent reduction in feature sizes in integrated circuit (IC) technology, leading to the need for increased placement of functional circuits on each chip. When it comes to the design of digital circuits, there is a significant focus on hybrid logic. Hybrid logic is highly regarded due to its ability to consume less power while achieving higher efficiency. Hybrid logic circuits have similarities to complementary metal-oxide-semiconductor (CMOS) transistors, yet possess a reduced transistor count while offering enhanced performance and reliability capabilities. This study examines the modeling and implementation hybrid multiplier with of help of hybrid adder. The functionality of adder is determined with the help of hybrid logic producing XOR/XNOR functionalities in single circuit.    The proposed hybrid Multiplier, which incorporates a hybrid Adder, has been successfully designed and implemented using CMOS 45nm technology and Mentor Graphics software the hybrid transistor logic multiplier demonstrates a decrease in total delay of 60% compared to CMOS

High-Performance Ternary (4:2) Compressor Based on Capacitive Threshold Logic

This paper presents a ternary (4:2) compressor, which is an important component in multiplication. However, the structure differs from the binary counterpart since the ternary model does not require carry signals. The method of capacitive threshold logic (CTL) is used to achieve the output signals directly. Unlike the previously presented similar structure, the entire capacitor network is divided into two parts. This segregation results in higher reliability and robustness against unwanted process, voltage, and temperature (PVT) variations. Simulations are performed by HSPICE and 32nm CNFET technology. Simulation results demonstrate about 94% higher performance in terms of power-delay product (PDP) for the new design over the previous one

A Survey on Approximate Multiplier Designs for Energy Efficiency: From Algorithms to Circuits

Given the stringent requirements of energy efficiency for Internet-of-Things edge devices, approximate multipliers, as a basic component of many processors and accelerators, have been constantly proposed and studied for decades, especially in error-resilient applications. The computation error and energy efficiency largely depend on how and where the approximation is introduced into a design. Thus, this article aims to provide a comprehensive review of the approximation techniques in multiplier designs ranging from algorithms and architectures to circuits. We have implemented representative approximate multiplier designs in each category to understand the impact of the design techniques on accuracy and efficiency. The designs can then be effectively deployed in high-level applications, such as machine learning, to gain energy efficiency at the cost of slight accuracy loss.Comment: 38 pages, 37 figure

Implementation of arithmetic primitives using truly deep submicron technology (TDST)

The invention of the transistor in 1947 at Bell Laboratories revolutionised the electronics industry and created a powerful platform for emergence of new industries. The quest to increase the number of devices per chip over the last four decades has resulted in rapid transition from Small-Scale-Integration (SSI) and Large-Scale-lntegration (LSI), through to the Very-Large-Scale-Integration (VLSI) technologies, incorporating approximately 10 to 100 million devices per chip. The next phase in this evolution is the Ultra-Large-Scale-Integration (ULSI) aiming to realise new application domains currently not accessible to CMOS technology. Although technology is continuously evolving to produce smaller systems with minimised power dissipation, the IC industry is facing major challenges due to constraints on power density (W/cm2) and high dynamic (operating) and static (standby) power dissipation. Mobile multimedia communication and optical based technologies have rapidly become a significant area of research and development challenging a variety of technological fronts. The future emergence or 4G (4th Generation) wireless communications networks is further driving this development, requiring increasing levels of media rich content. The processing requirements for capture, conversion, compression, decompression, enhancement and display of higher quality multimedia, place heavy demands on current ULSI systems. This is also apparent for mobile applications and intelligent optical networks where silicon chip area and power dissipation become primary considerations. In addition to the requirements for very low power, compact size and real-time processing, the rapidly evolving nature of telecommunication networks means that flexible soft programmable systems capable of adaptation to support a number of different standards and/or roles become highly desirable. In order to fully realise the capabilities promised by the 4G and supporting intelligent networks, new enabling technologies arc needed to facilitate the next generation of personal communications devices. Most of the current solutions to meet these challenges are based on various implementations of conventional architectures. For decades, silicon has been the main platform of computing, however it is slow, bulky, runs too hot, and is too expensive. Thus, new approaches to architectures, driving multimedia and future telecommunications systems, are needed in order to extend the life cycle of silicon technology. The emergence of Truly Deep Submicron Technology (TDST) and related 3-D interconnection technologies have provided potential alternatives from conventional architectures to 3-D system solutions, through integration of IDST, Vertical Software Mapping and Intelligent Interconnect Technology (IIT). The concept of Soft-Chip Technology (SCT) entails integration of Soft• Processing Circuits with Soft-Configurable Circuits . This concept can effectively manipulate hardware primitives through vertical integration of control and data. Thus the notion of 3-D Soft-Chip emerges as a new design algorithm for content-rich multimedia, telecommunication and intelligent networking system applications. 3•D architectures (design algorithms used suitable for 3-D soft-chip technology), are driven by three factors. The first is development of new device technology (TDST) that can support new architectures with complexities of 100M to 1000M devices. The second is development of advanced wafer bonding techniques such as Indium bump and the more futuristic optical interconnects for 3-D soft-chip mapping. The third is related to improving the performance of silicon CMOS systems as devices continue to scale down in dimensions. One of the fundamental building blocks of any computer system is the arithmetic component. Optimum performance of the system is determined by the efficiency of each individual component, as well as the network as a whole entity. Development of configurable arithmetic primitives is the fundamental focus in 3-D architecture design where functionality can be implemented through soft configurable hardware elements. Therefore the ability to improve the performance capability of a system is of crucial importance for a successful design. Important factors that predict the efficiency of such arithmetic components are: • The propagation delay of the circuit, caused by the gate, diffusion and wire capacitances within !he circuit, minimised through transistor sizing. and • Power dissipation, which is generally based on node transition activity. [2] Although optimum performance of 3-D soft-chip systems is primarily established by the choice of basic primitives such as adders and multipliers, the interconnecting network also has significant degree of influence on !he efficiency of the system. 3-D superposition of devices can decrease interconnect delays by up to 60% compared to a similar planar architecture. This research is based on development and implementation of configurable arithmetic primitives, suitable to the 3-D architecture, and has these foci: • To develop a variety of arithmetic components such as adders and multipliers with particular emphasis on minimum area and compatible with 3-D soft-chip design paradigm. • To explore implementation of configurable distributed primitives for arithmetic processing. This entails optimisation of basic primitives, and using them as part of array processing. In this research the detailed designs of configurable arithmetic primitives are implemented using TDST O.l3µm (130nm) technology, utilising CAD software such as Mentor Graphics and Cadence in Custom design mode, carrying through design, simulation and verification steps