VLSI research papers IEEE PAPER

VLSI, ASIC, SOC , FPGA, VHDL-Very-large-scale integration (VLSI) is the process of creating integrated circuits by combining thousands of transistors into a single chip.
An integrated circuit or monolithic integrated circuit (also referred to as IC, chip, or microchip) is an electronic circuit manufactured by lithography, or the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material. Additional materials are deposited and patterned to form interconnections between semiconductor devices.
Integrated circuits are used in virtually all electronic equipment today and have revolutionized the world of electronics. Computers, mobile phones, and other digital home appliances are now inextricable parts of the structure of modern societies, made possible by the low cost of production of integrated circuits.

vlsi projects

updated july 2020

vlsi design automation

dct discrete cosine transform architecture vlsi project

fft fast fourier transform processor vlsi project

differentiator vlsi project

high speed comparator vlsi project

binary to gray code converter vlsi project

clock gating vlsi project

cmos flip flop vlsi project

full adder vlsi project

multiplexer vlsi project

mac unit design vlsi project

digital signal processor vlsi project

rtl projects vlsi project

vlsi layout

sram layout vlsi project

dram dynamic random access memory design vlsi project

sram design vlsi project

parallel processor architecture vlsi project

vedic multiplier vlsi project

digital filter vlsi project

iir filter matlab vlsi project

fir filter in matlab vlsi project

floating point multiplier vlsi project

design of 16 bit multiplier vlsi project

fifo first input first output buffers buffer design vlsi project

high speed accelerator vlsi projects

multiplier architecture vlsi projects

montgomery modular multiplication vlsi projects




nanotechnology 2020

cmos 2020

fpga field programmable gate array 2020

vlsi very large scale integration 2020

sensor 2020

fpga field programmable gate array 2020

vlsi very large scale integration 2020







VLSI 2018


VLSI 2018







VHDL 2018

















SOC-system on chip-2015


ADC-Analog to digital converter-2015



nems-2015 LOW POWER-VLSI

SOC-system on chip
VLSI layout
SOC-system on chip
SOC-system on chip
DSP-digital signal processing
Analog layout
VLSI layout
Analog to digital converter
digital to analog converter




nano technology

VLSI simulation projects

vlsi conferences
ISSCC IEEE International Solid-State Circuits Conference
CICC IEEE Custom Integrated Circuits Conference
ISCAS IEEE International Symposium on Circuits and Systems
VLSI Circuits IEEE Symposium on VLSI Circuits
VLSI IEEE International Conference on VLSI Design
DAC Design Automation Conference
ICCAD International Conference on Computer-Aided Design
ISPD International Symposium on Physical Design
ISQED International Symposium on Quality Electronic Design
DATE Design Automation and Test in Europe
IEDM IEEE International Electron Devices Meeting
ASP-DAC Asia and South Pacific Design Automation Conference

very large scale integrated circuitry Johns Hopkins University
free download

Very large scale integrated circuitry is playing a key role in the development of modern electronic sys- tems at APL. program, called the Very High Speed Integrated Circuit . (VHSIC) part of Independent Research and Development efforts.

The Very Large Scale Integrated Circuit: By making jstor
free download

especially interested in very high order computer languages and functional decomposition This very large scale integrated circuit , magnified about. 25 times, combines information-processing systems, research in artificial intelligence, and

free download

be prepared in order to guide research on computer structures. Therefore 5. logic functions, especially Semiconductor memory arrays which form a very From the discussion above it seems clear that a Large Scale Integrated circuit chip .

Very-Large-Scale Integration Of Electronic Circuits eolss
free download

Keywords: VLSI, Very large scale integration, integrated circuit design, extensions or modifications, must be targeted in modern days VLSI research .

Large Scale Integrated Circuits Technology State of the Art and
free download

oxide semiconductor fet (mosfet) used in the ultra large scale integrated circuit (ulsic). Introduces a new and growing research area on the intersection of

Designing Issues Associated With Very Large Scale ijcst
free download

Small Scale Integrated Circuits , Very Large Scale Integrated. Circuits, Ultra on a single chip . It was the time when the cost of research began to decline and.

IEEE Xplore Full-Text tvlsi Duke University
free download

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) Scientist with the Intel Labs- Circuits Research Laboratory, Hillsboro, OR, USA,

Very Large Scale Integration hardware> (VLSI) A term
free download

1 2003 Very Large Scale . Integration. hardware> integrated circuits composed of Research Lab and current activities underway. This will be. IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 1 NO. JANUARY and Systems Society and the IEEE Solid State Circuits Society. He has made significant research contributions in VLSI design

From imitation to innovation : the very large scale integrated
free download

t fchnological organization discussed here is the Very Large Scale Integrated . (VLSI) Technology Research Association, which was the central organization of four-year VLSI project VLSI circuits are the nextgeneration of semiconductors

the soviet microelectronics industry CIA
free download

The USSR has an acute shortage of very - large - scale integrated (VLSI) circuits. Coordinating research and production efforts with East European mem- bers of the The Soviets are having trouble producing ICs at the VLSI level, in large.

Vlsi System Design When And How To Design Very Large Scale
free download

Design When And How To Design Very Large Scale Integrated Circuits by Sarah. Kuester Study Group Discover them in kindle, zip, , ppt, rar, txt, and also Street, London W1. tFor IC read Integrated Circuit , and for LSI read Large Scale by too much emphasis on basic research and too little on development and

Ajay Joshi Boston University
free download

A. Joshi, CNS: CSR Collaborative Research : Leveraging Intra- chip /Inter- chip Feedback Equalization IEEE Transactions on Very Large Scale Integration

Two-Dimensional and Three-Dimensional Integration Core
free download

from 2-D planar system-on-a- chip -type single- chip solutions to al- ternatives such as tiled silicon Agency (SIDA) under the auspices of the research capacity building project not require many interconnection levels, resulting in a very high packing package-on-package design guidelines, Chip Scale Rev., no. . Jul.

Moores Law PDH Online
free download

Very Large - Scale Integration . is the observation that the number of transistors on an integrated circuit (or microprocessor) doubles every two years.

A Practical and Efficient Integrated System for CiteSeerX
free download

Abstract--This paper studies and implements an integrated system for VLSI/ULSI ultra large scale integrated circuit (VLSI/ULSI) technology has profoundly

Wave-pipelining: A Tutorial And Research Survey Very
free download

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. NO. circuit design which implements pipelining in logic without the.

Workshops on Extreme Scale Design Automation arXiv
free download

depth and scale of on- chip integration, electronic system-level integration, the increasing Extreme- scale Electronic Design Automation research is a big -data discipline that remains The Electronic Design Automation (EDA) of very large -.

Grids in Very Large Scale Integration Systems UR Research
free download

To de- velop complex integrated circuits ( IC ) in the late 1960s and early 1970s, companies utilized a large number of engineers and technicians to manually craft

Integrated Circuits DiVA
free download

me as a research associate in Lancaster University under the EU-FP7 funded to Very Large Scale Integration (VLSI) 1990s, and to Giga-Scale Integration (GSI).

Targeting the Computer
free download

research and development in Japans universities and colleges has grown notes that none of the hojokin for the very large scale integrated circuit (VLSI)

Very Large Scale Integration (VLSI) University of Arizona
free download

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. tion of three-dimensional (3-D) integrated circuits ( ICs ) is derived MARCO Focused Research Center on Interconnects which was funded at the.

study on integrated circuit IDC Technologies
free download

Wafer- scale integration (WSI) is a system of building very - large integrated circuits that uses an entire silicon wafer to produce a single super- chip . Through a

Chapter 1: Introduction Shodhganga
free download

electronic device for Very . Large Scale Integrated (VLSI) circuits such as in microprocessors and semiconductor or so called high-k dielectrics is a part of these research efforts. single chip . The era of Very Large Scale Integration (VLSI).

Design Methodology of Very Large Scale Integration ucf stars
free download

Evolution of CAD/CAM in IC Design and Production CAD Supported IC INTRODUCTION. This research report discusses VLSI ( Very Large Scale Integra-.by AD Oberai ‎1983 A.F. Murray and H.M. Reekie, Integrated Circuit Design. F.J. Owens integration (LSI), 10000 devices (1980), to very large scale integration. (VLSI), 1 million Final Year Design Study undertaken by students on the BEng Electronics and.

Power Noise in TSV-Based 3-D Integrated Circuits Drexel
free download

planes . An important issue for 3-D integrated circuits ( ICs ) is the de- State Office of Science, Technology and Academic Research to the Center for. Advanced Chair of the IEEE Transactions on Very Large Scale Integration (VLSI) Sys-.

Device and material requirements in very large scale
free download


A Systems Engineering Approach for Artificial Intelligence
free download

This paper reviews the very large scale integration (VLSI) revolution enabled by Mead and Conway in the late 1970s and components per integrated circuit doubled every year and a major Ad- vanced Research Projects Agency (ARPA).

On stochastic modelling of very large scale integrated circuits
free download

very large scale integrated circuits . Variations in fabrication Part Two: Methods completes an study of existing methods which are, or which might be, used to

The Future of Integrated Circuits: A Survey of Nano-electronics
free download

( circuits built with components on the scale of 10nm) seem to be the most When the doping material has an extra electron, the majority carrier are electrons. In this paper, we consider the major research efforts for nano-electronics by

Large-scale integration: Promis versus accomplishments
free download

to integrated circuits to large - scale integration, describes some of the on one chip Laboratory researchers continued to apply their in- LSI circuits really are.

International Journal of Innovative Technology and IJITEE
free download

1 2020prominent research papers and discuses FPGA architecture Design and Development of a Very Large Scale Integrated Circuit Architecture

Key Steps to the Integrated Circuit SMTnet
free download

manium and silicon transistors to the current metal-oxide semiconductor IC products. Also described are transistor logic. VLSI very large scale integration

Advanced Fabrication Processes for Superconducting Very
free download

Quantum (SFQ) digital circuits with very large scale integration . (VLSI) on 200-mm (PECVD) system Sequel from Novellus (Lam Research . Corporation).

Counterfeit Integrated Circuits UT Dallas
free download

However, not enough research has yet addressed the detection and avoidance of all Contemporary advancements in very large scale in- tegration Counterfeit Integrated Circuits : A Rising Threat in the Global Semiconductor Supply Chain.

Research on the Effective Detection Methods of Large Scale
free download

of manufacturing process, large scale integrated circuits ( ICs in abbreviation and IC tests occupy a very large proportion in the total cost, so the expensive testby J Li ‎2015

integrated circuit performance prediction with outlier
free download

A possible application of this research for burn-in and test cost reduction is discussed. The journal model is IEEE Transactions on Very Large Scale Integration

Robust Design-for-Security Architecture for Enabling Trust in
free download

exception of pagination. IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS. 1 ufacturing, most system-on- chip design companies outsource researchers have proposed different metering and obfuscation.

Figures-of-Merit to Evaluate the Significance of Switching
free download

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 2 NO. Index Terms Analog-digital integrated circuits , circuit noise, Office of the Vice President for Research through the Stony Brook University,.

Open Source Cell Library Mono3D to Develop Large-Scale
free download

cuits ( ICs ) achieve ultra - high density device integration through fine-grained Thus, circuit-level research on monolithic 3D technology has significantly grown

Electrical Computer Engineering (ECE) UNH Catalog
free download

Credits: 4. Principles of VLSI ( Very Large Scale Integration ) systems at the physical level. CMOS circuit and logic design, CAD tools, CMOS system case studies .

Application of VLSI in Artificial Intelligence IOSR Journal
free download

This paper describes the application of VLSI ( Very Large Scale Integrated ) circuit and today with the advent of the computer and 50 years of research into AI

A GUI-based Integrated Circuit Floorplanning Environment for
free download

to use tool, QUILT is well suited for both research and coursework purposes. 1. counts, rough floorplanning for very large scale integration . (VLSI) layout

DiVision of circUits anD sYsteMs EEE, NTU
free download

circuit ( IC ) designers and researchers to propel the To scale greater heights in IC research , the division ultra - wide -band (UWB) radio channel allows it to.

Integrated Circuit Test Engineering
free download

T-Spice is the trademark of Tanner Research , Inc., 2650 East Foothill Blvd. Rents Rule , IEEE Transactions on Very Large Scale Integration (VLSI). Systems

Buffer block planning for interconnect planning and prediction
free download

Abstract This paper studies buffer block planning (BBP) for interconnect planning FOR deep submicron (DSM) very large scale integrated. (VLSI) designs, it is high-performance integrated circuit ( IC ) designs (e.g., close to 800000 for the.

VLSI Circuits Emerging Applications (Devices, Circuits, and Systems
free download

Vlsi and post-cmos electronics is a useful reference guide for researchers , engineers and very - large - scale integrated (vlsi) circuits , vlsi: circuits for emerging

free download

Very High Speed Integrated Circuits (VHSIC); many industrial contractors in this program are long-range research effort on very large scale integration. Further

A Historical Review of Circuit Simulation Oregon State EECS
free download

problem, consider todays very - large - scale -integrated. (VLSI) circuit [16], [39], and system researchers have attacked the PCB and IC placement and routing

M.TECH VLSI DESIGN Department of Electronics and
free download

Very Large Scale Integrated (VLSI) Circuit Design is the process of designing a gates and to study the issues and methodologies involved in the integration of

Government-University-Industry collaborations on VLSI
free download

and the vital role of the Defense Advanced Research Projects Agency Efforts to develop very large scale integrated circuit (VLSI) technology demonstrate the.by EF CHAPTER

free download

Integrated Circuit Design Techniques Hierarchical Design, Design. Abstraction and Test Bench, Simulation and Synthesis issues, case study of ALU/. Sequence ? Very - large - scale integration (VLSI) is the process of creating an integrated

Three-Dimensional Integrated Circuits
free download

Recent Research Results in 3D ICs at NanoCAS Lab Scale supply and threshold E. Salman and E. G. Friedman, High Performance Integrated Circuit Design, for TSV-based 3D ICs with Power Gating, IEEE Transactions on Very Large .

Interconnect Lifetime Prediction for Reliability-Aware Systems
free download

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 1 NO. dependence of leakage power, circuit performance, IC package MRL, by the Army Research Office (ARO) under Grant W911NF-04-1-028 .

Carbon Nanotube Interconnect Modeling for Very Large Scale
free download

study carbon nanotube for on- chip wire inductors and it application in design of LC large - scale CNT based integrated circuits . The viability of CNT-FET circuits

vlsi and fabrication BioInfo Publication
free download

World Research Journal of Telecommunications Systems. ISSN: 2278-8573 Key words- VLSI ICs , VLSI chip makers, IC - fabrication, Wafer manufacturing, semiconductor Very - large - scale integration (VLSI) is the process of creating inte-.

Basic Research Needs for Microelectronics DOE Office of
free download

information between different parts of a computer chip at high speeds and low at high spatial and depth resolution and at temporal scales down to the ultra -.

Basic Limitations in Microcircuit Fabrication Technology
free download

if any, research ARPA might sensibly conduct in integrated microcircuit technology. The authors of very - large - scale integrated circuits . Indications are that

integrated circuit Ideas to Integrated Circuits
free download

2 2010 Very large - scale integration (VLSI) vastly increased circuit This was followed by large scale integration techniques, or LSI, which produced ICs with thousands of This design work require research and development of

Analysis of blocking dynamic circuits Very Large Scale
free download

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) circuits , cascading low-skew dynamic gates allows each dynamic gate to tol- Advanced Research Projects Agency (DARPA) under Contract MDA972-02-1-. 0004.

Introduction to ASIC Design TCE
free download

ULSI ( Ultra Large - Scale Integration)-(late 1980). More than about one million circuit elements on a single chip . The Intel 486 and Pentium microprocessors,

Integrated Circuits Elevator Books
free download

How to troubleshoot and repair ICs in elevator controllers. Learning very - large - scale integration and ultra -large- universities and large research facilities.

Evaluation of Smart Chip Technology NJ.gov
free download

To propose, build, and test a very large scale integration design and implementation Integrated Circuit (VLSI ASIC) is used to provide a high quality gas recognition system. However NJDOT Research Report No: FHWA-NJ-2003-010.

Fast Electromagnetics-Based Co-Simulation of Linear
free download

The proposed simulator has been applied to co-simulate on- chip interconnects and the very large - scale integration (VLSI) community, it has to be fast enough to be put into co-simulation algorithms have been developed, the research on.

Toward an analog very large scale integration system for
free download

across the DTMP chip , which is equivalent to the perceived velocity, can be used to Subject terms: depth perception; motion parallax; analog very large scale integra- dous progress in this field; researchers have developed a number of

biographical sketch Home | Electrical and Computer
free download

Research and Development Engineer, Summer 2006 and Summer 2007 Book. 1. E. Salman and E. G. Friedman, High Performance Integrated Circuit Design, Mc-Graw Hill, Transactions on Very Large Scale Integration (VLSI) System, Vol.

Low-power operation using self-timed circuits and DTU Orbit
free download

Published in: I E E E Transactions on Very Large Scale Integration Systems C. Niessen and C. H. van Berkel are with Philips Research Laboratories,. 5656 AA

A Critical Research Analysis on Low Power Very Large Scale
free download

Research Scholar, Dr.APJ Abdul Kalam Technical University, Lucknow, U.P., India. Abstract: Testing low power very large scale integrated (VLSI) circuits in the

Full Text: Swarup Bhunia
free download

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 1 NO. This work was supported in part by Marco Gigascale System Research Center the working (i.e., free from manufacturing defects) ICs based.

free download

Springing from the invention of the transistor in 1947 and the integrated circuit in technology becomes more complex with VLSI ( very large - scale integration),

The NBS semiconductor technology program and VLSI
free download

ment, design, and production of transistors and integrated circuits since their invention. The trend to The National Bureau of Standards (NBS), as theNations research labora- for Very Large Scale Integration (VLSI) beginning late in 1980.

atmospheric instrumentation American Meteorological Society
free download

(an Integrated Circuit or IC ) replace large circuit i The National Center for Atmospheric Research is spon- sored by the The 70s brought Large Scale Integration (LSI) of devices, both becoming very attractive in cost, will make isopleth

Transistor Degradations in Very Large-Scale-Integrated
free download

expanded to a few billions, called very large - scale integration (VLSI) or ultra device and circuit research to develop power-efficient and degradation-aware low

The VLSI revolution at MIT by Paul Penfield, Jr. icdst
free download

In the late 1970s the VLSI ( Very Large Scale Integration) revolu- tion opened up the design of integrated circuits to people who did not know anything about

very large scale integration cell based path extractor for
free download

I would like to express my deepest gratitude to my academic and research 2.3 Data Extraction Method in Very Large Scale Integration Integrated Circuit .

Shiva Shankar Ramani UAB
free download

Domain Logic Circuits , IEEE Transactions on Very Large Scale Integration K. Lingasubramanian and S. Bhanja, An Error Model to Study the Behavior of

VLSI and Pipeline International Journal of Engineering
free download

Proper study can help to take advantages of technology. Key words: IC , VLSI, Micro Processors, Pipeline. I. INTRODUCTION. Very - large - scale integration (VLSI)

Skill needs in VLSI circuits SAGE Journals
free download

The forecast need for designers of Very Large Scale Integrated Circuits is described. The article By the late 1980s, studies had shown that the ECs academicby K W lcken ‎1992

Test and characterization methodologies for advanced
free download

2018to open new avenues for research in the domains of digital circuit design progression from Small Scale Integration (SSI) to Very Large Scale

Publications (as of 2 2020) Books 1. G. De Micheli, A
free download

G. De Micheli, Giovanni, S. Mir and R. Reis, Editors VLSI-SoC: Research Trends in Timing Analysis of Large Scale Circuits , IEEE Transactions on CAD/ICAS, Vol. in IEEE Transactions on very Large Scale Integration (VLSI) Systems, vol.

Design and Implementation of Ternary Logic Integrated
free download

2019 integrated circuit doubles every two years), the logic data density in density in practical integrated circuits , further research on ternary Finally, we will focus on the design of large scale ternary integrated we can tune the middle output logic level to be very high for the PTI (Figure 2c) or very low for the.

Dylan Stow Scalable Energy-efficient Architecture Lab
free download

Minor: Very Large Scale Integration (VLSI) and Computer Aided Design (CAD) research interests include the areas of computer architecture, VLSI circuit

Low-Power Clock Branch Sharing Double-Edge Triggered
free download

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, P. Zhao and R. A. Barcenas are with the Integrated Circuit Design and Em- puter Studies , University of Louisiana at Lafayette, Lafayette, LA 70504 USA.

LinkPDF UC Press Journals
free download

recent research activities in laboratories around the world. Essentially, it is the 3 Thus it is understandable that when the Soviet Union undertook large - scale ogy is judged to be several years behind the U.S. and highly imitative featured integrated circuit technology, larger and faster memories, modularity in design

A Compact Transregional Model for Digital CMOS Circuits
free download


Koushik Chakraborty USU Engineering Utah State University
free download

Research . Interests. VLSI Design and Automation, Circuit -Architectural Co-design. IEEE Transactions on Very Large Scale Integration Systems (TVLSI).

Editorial Commentry
free download

paper be detected years later, subjecting the research supervisor to a great modern high-density Very Large Scale Integrated circuits is the integration of

MEMS-Enabled Silicon Photonic Integrated Devices and Circuits
free download

2019tems, nanophotonics, photonic integrated circuits , silicon photonics. Unions Horizon 2020 Research and Innovation Programme (MORPHIC) at very large scale allows in particular to conceive fully recon- figurable

(177 KB)
free download

Paper type Research paper. 1. Introduction. Adders of various bit-widths are frequently required in very large - scale integrated circuits (VLSI) from processors to.

Vlsi Design 1e alfabeto.dk
free download

very large scale integration vlsi is the process of creating an integrated circuit ic by india with a focus on engineering education research over the years the

Curriculum Vitae University of Utah
free download

Research Assistant Professor ECE Department, University of Illinois at Urbana-Champaign Develop large - scale software systems with a specific focus on parallel 2nd Place, National Collegiate IC /CAD Programming Contest, Ministry of T.-W. Huang, P.-C. Wu, and Martin D. F. Wong, UI-Timer: An Ultra -Fast Clock

Rapid Statistical Timing Analysis of Integrated Circuits to Test
free download

The Wisconsin Alumni Research Foundation (WARF) is seeking commercial very large scale integrated (VLSI) circuits , which contain 100,000 to 1 million

Electro-thermal And Logi-thermal Simulation Of Vlsi Designs
free download

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. NO. integrated circuits the need for reliable and quick thermal, His research field is electro-thermal simulation of VLSI integrated circuits ,.

A test evaluation technique for vlsi circuits using register
free download

For a system timing controller application specific integrated circuit , the stratified RTL Test patterns for large very large scale integration (VLSI) systems are often of a circuit. Some of the previous research in the area of high-level fault-mod-.

Computer Engineering (4450)
free download

sequential circuits . Laboratory 4450:301 Undergraduate Research I: Computer Engineering (1 Credit) circuits . Very large scale integration (VLSI) fabrication.

Chip Basics: Time, Area, Power, Reliability and Configurability
free download

With increases in chip frequency and especially in transistor density, the designer must be able to VLSI ( Very Large Scale Integration) complexity theorists have shown that an A T n ning of the study of optimization of design alternatives.

Authors Kit SMU
free download

A VLSI ( Very Large Scale Integration ) circuit contains a large number of In addition to design with CAD tools, the graduate students research current methods

Application of VLSI Technology in Wireless Mobile IJRASET
free download

International Journal for Research in Applied Science Engineering Technology (IJRASET). ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor:6.887 systems are suitable for implementation under VLSI ( Very Large Scale Integration).