Slide 1Slide 2Slide 3Slide 4Prerequisite knowledgeSlide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29ECE 645 CAD Tool FlowsSlide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Kris GajOffice hours: Monday, 6:00-7:00 PM Tuesday, Thursday, 4:30-5:30 PM, and by appointmentResearch and teaching interests:• cryptography• computer arithmetic• VLSI design and testingContact:Science & Technology II, room 223 [email protected] (703) 993-1575ECE 645Part of:MS in EEMS in CpEDigital Systems Design – pre-approved courseOther concentration areas – elective course Certificate in VLSI Design/ManufacturingPhD in ITPhD in ECEMS CpE: DIGITAL SYSTEMS DESIGNConcentration advisors: Kris Gaj, David Hwang, Ken Hintz1. ECE 545 Digital System Design with VHDL– D. Hwang, K. Gaj, project, FPGA design with VHDL, Aldec/Synplicity/Xilinx2. ECE 645 Computer Arithmetic– K. Gaj, D. Hwang, project, FPGA design with VHDL or Verilog, Aldec/Synplicity/Xilinx3. ECE 681 VLSI ASIC Design – N. Klimavicz, project/lab, back-end ASIC design with Synopsys tools4. ECE 586 Digital Integrated Circuits – D. Ioannou, Q. LiPrerequisitesPermission of the instructor, granted assuming that you knowVHDL or Verilog, High level programminglanguage(preferably C)ECE 545 Introduction to VHDLorPrerequisite knowledge•This class assumes proficiency with the FPGA CAD tools from ECE 545•You are expected to be proficient with:–Synthesizable VHDL coding–Advanced VHDL testbenches, including file input/output–Xilinx FPGA synthesis and post-synthesis simulation–Xilinx FPGA place-and-route and post-place and route simulation–Reading and interpreting all synthesis and implementation reportsCourse web pageECE web page  Courses  Course web pages  ECE 645http://ece.gmu.edu/coursewebpages/ECE/ECE645/S09/Computer ArithmeticLecture ProjectProject 1 20 %Project 2 30 %Homework 10 %Midterm exam (in class) 15 %Final Exam (in class) 25 %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 baseAt the end of this course you should be able to:• Understand mathematical and gate-level algorithms for computer addition, subtraction, multiplication, division, and exponentiation• Understand tradeoffs involved with different arithmetic architectures between performance, area, latency, scalability, etc.• Synthesize and implement computer arithmetic blocks on FPGAs• Be comfortable with different number systems, and have familiarity with floating-point and Galois field arithmetic for future study• Understand sources of error in computer arithmetic and basics of error analysisThis knowledge will come about through homework, projects and practice exams.Course ObjectivesLecture 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 dividersLONG INTEGER ARITHMETIC1. Modular Exponentiation2. Multi-Precision Arithmetic in SoftwareFLOATING POINT AND GALOIS FIELD ARITHMETIC1. Floating-point units2. Galois Field GF(2n) unitsPossible 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 ArithmeticLiterature (1)Required textbooks:Behrooz Parhami, Computer Arithmetic: Algorithms and Hardware Design, Oxford University Press, 2000.Jean-Pierre Deschamps, Gery Jean Antoine Bioul, Gustavo D. Sutter, Synthesis of Arithmetic Circuits: FPGA, ASIC and Embedded Systems, Wiley-Interscience, 2006.Literature (2)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:1. Volnei A. Pedroni, Circuit Design with VHDL, The MIT Press, 2004.2.Sundar Rajan, Essential VHDL: RTL Synthesis Done Right, S & G Publishing, 1998.VHDL books: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.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, 7/00, 3/05. 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• analysis of computer arithmetic algorithms and implementations• design of small hardware units using VHDL or VerilogMidterm examsMidterm Exam - 2 hrs 30 minutes, in class multiple choice + short problemsFinal Exam – 2 hrs 45 minutes comprehensive conceptual questions, analysis and design of arithmetic unitsPractice exams on the webMidterm Exam - Monday, March 23Final Exam - Monday, May 11Tentative days of exams:Project (1)Project I (20% of