Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Levels of design descriptionRegister Transfer Logic (RTL) Design DescriptionRTL Block Synthesis*VHDL Design StylesSlide 39Slide 40Slide 41Slide 42Slide 43Design EnvironmentSlide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Slide 60Learn to deal with approximationsSlide 62Consequences of bad approximationsSlide 64Slide 65Slide 66Slide 67Slide 68Kris GajOffice hours: Monday, 7:30-8:30 PM Thursday, 7:30-8:30 PMResearch and teaching interests:• cryptography• computer arithmetic• VLSI design and testingContact:Science & Technology II, room 223 [email protected], [email protected], (703) 993-1575ECE 645Part of:MS in EEMS in CpEDigital Systems Design – required courseOther concentration areas – elective course Certificate in VLSI Design/ManufacturingPhD in ITPhD in ECESpring 2006 Enrollment as of January 23, 2006MS in CpE7MS in EE6BS in CpE1PhD in ECE1PhD in IT1MS in ISA1NDG1DIGITAL SYSTEMS DESIGNConcentration advisor: Ken Hintz1. ECE 545 Introduction to VHDL – K. Gaj, K. Hintz, project, VHDL, Aldec/Synplicity/Xilinx and ModelSim/Synopsys2. ECE 645 Computer Arithmetic: HW and SW Implementation – K. Gaj, project, VHDL, Aldec/Synplicity/Xilinx and ModelSim/Synopsys3. ECE 586 Digital Integrated Circuits – D. Ioannou4. ECE 681 VLSI Design Automation – T. Storey, project/lab, back-end design with Synopsys toolsalgorithmicDesign levelregister-transfergatetransistorlayoutdevicesCoursesComputerArithmeticIntroduction to VHDLDigitalIntegratedCircuitsECE545ECE645ECE 586ECE 684MOS Device ElectronicsVLSI Design AutomationECE681Semiconductor Device Fundamentals ECE 584PrerequisitesPermission of the instructor, granted assuming that you knowVHDL or Verilog, High level programminglanguage(preferably C)ECE 545 Introduction to VHDLorCourse web pageECE web page  Courses  Course web pages  ECE 645http://teal.gmu.edu/courses/ECE645/index.htmComputer ArithmeticLecture ProjectProject 1 20 %Project 2 30 %Homework 15 %Midterm exam 1 (in class) 20 %Midterm exam 2 (take-home) 15 %Advanced digital circuit design course covering• addition and subtraction• multiplication• division and modular reduction• exponentiationEfficientIntegersunsigned and signedReal numbers• fixed point• single and double precision floating pointElementsof the Galoisfield GF(2n)• polynomial baseLecture topics (1)1. Applications of computer arithmetic algorithms2. Number representation• Unsigned Integers• Signed Integers• Fixed-point real numbers• Floating-point real numbers• Elements of the Galois Field GF(2n)INTRODUCTION1. Basic addition, subtraction, and counting2. Carry-lookahead, carry-select, and hybrid adders3. Adders based on Parallel Prefix NetworksADDITION AND SUBTRACTIONMULTIOPERAND ADDITION1. Carry-save adders2. Wallace and Dadda Trees3. Adding multiple signed numbersMULTIPLICATION1. Tree and array multipliers2. Sequential multipliers3. Multiplication of signed numbers and squaringDIVISION1. Basic restoring and non-restoring sequential dividers2. SRT and high-radix dividers3. Array dividersFLOATING POINT AND GALOIS FIELD ARITHMETIC1. Floating-point units2. Galois Field GF(2n) units• University of California, Santa Barbara, Behrooz Parhami, ECE252B: Computer Arithmetic. • University of Massachusetts, Amherst, Israel Koren, ECE666: Digital Computer Arithmetic • Lehigh University, Michael Schulte, ECE496: High-Speed Computer Arithmetic. • Worcester Polytechnic Institute, Berk Sunar, EE-579 V Computer Arithmetic Circuits.• Stanford University, Michael Flynn, EE486: Advanced Computer Arithmetic. • University of California, Davies, Vojin Oklobdzija, ECE278: Computer Arithmetic for Digital Implementation. Similar courses at other universitiesNew in this course• real-life project based on VHDL or Verilog HDL• operations in the Galois Field (with the application in cryptography and communications)Possible topics for a Scholarly Paper or Research Projectfor the CpE & EE students Advanced Computer ArithmeticSquare rootExponential and logarithmic functionsTrigonometric functionsHyperbolic functionsFault-Tolerant ArithmeticLow-Power ArithmeticHigh-Throughput ArithmeticThree Curriculum OptionsMS ThesisOptionResearch Project OptionScholarly PaperOption2 corecourses4 requiredcourses2 electivecourses3 electivecourses4 electivecoursesECE 799 Master’s Thesis (6 cr. hrs)ECE 798 Research ProjectScholarly paperScholarly paperLiterature (1)Required textbook:Behrooz Parhami, Computer Arithmetic: Algorithms and Hardware Design, Oxford University Press, 2000. Milos D. Ercegovac and Tomas Lang Digital Arithmetic, Morgan Kaufmann Publishers, 2004.Isreal Koren, Computer Arithmetic Algorithms, 2nd edition, A. K. Peters, Natick, MA, 2002.Recommended textbooks:Literature (2)1. Sundar Rajan, Essential VHDL: RTL Synthesis Done Right, S & G Publishing, 1998.2. Volnei A. Pedroni, Circuit Design with VHDL, The MIT Press, 2004.VHDL books (used in ECE 545 in Fall 2005)Literature (3)Supplementary books: 1. E. E. Swartzlander, Jr., Computer Arithmetic, vols. I and II, IEEE Computer Society Press, 1990. 2. Alfred J. Menezes, Paul C. van Oorschot, and Scott A. Vanstone, Handbook of Applied Cryptology, Chapter 14, Efficient Implementation, CRC Press, Inc., 1998. 3. Christof Paar, Efficient VLSI Architectures for Bit Parallel Computation in Galois Fields, VDI Verlag, 1994.Literature (3)Proceedings of conferences ARITH - International Symposium on Computer Arithmetic ASIL - Asilomar Conference on Signals, Systems, and Computers ICCD - International Conference on Computer Design CHES - Workshop on Cryptographic Hardware and Embedded Systems Journals and periodicals IEEE Transactions on Computers, in particular special issues on computer arithmetic: 8/70, 6/73, 7/77, 4/83, 8/90, 8/92, 8/94. IEEE Transactions on Circuits and Systems IEEE Transactions on Very Large Scale Integration IEE Proceedings: Computer and Digital Techniques Journal of VLSI Signal ProcessingHomework• reading assignments (main textbook + articles)• analysis of hardware