Schedule of Project Presentations
Monday, May 12, 6:00-9:20pm
The Nguyen Engineering Building, room 3507
|Time and location:||Wednesday, 4:30-7:10 PM, Aquia Building, room 219|
|Email:||kgaj (at) gmu.edu|
|Office hours:||Monday, Wednesday, 3:00-4:00 PM; Wednesday, 7:30-8:30 PM; and by appointment|
Behrooz Parhami, Computer Arithmetic: Algorithms and Hardware Design, 2nd Edition, Oxford University Press, New York, 2010.
Gery Jean Antoine Bioul, Gustavo D. Sutter, Synthesis
Arithmetic Circuits: FPGA, ASIC and Embedded Systems,
Joseph Cavanagh, Computer
Arithmetic and Verilog HDL Fundamentals, CRC Press,
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.
Sundar Rajan, Essential VHDL: RTL Synthesis Done Right, S & G Publishing, 1998.
Software Packages Used in This Class
Course Outline (subject to possible modifications):
Lecture 11: Advanced Dividers. [PPT, PDF]
Lecture 10: Basic Dividers. [PPT, PDF]
Radix 2 Restoring Divider (unsigned): diagram 1, diagram 2
Radix 2 Non-Restoring Divider (unsigned): diagram
Lecture 9: High-Radix Sequential Multipliers. Bit-Serial Multipliers. Modular Multipliers. [PPT, PDF]
Radix 4 Sequential Multiplier with Booth Encoding without CSA (unsigned a and x): diagram, recoding logic
Radix 4 Sequential Multiplier with Booth Encoding with CSA (unsigned a, signed x): diagram 1, diagram 2
Lecture 8: FPGA Multipliers. Radix 2 Sequential Multipliers. [PPT, PDF]
FPGA Multipliers: diagram 1, diagram 2, diagram 3
Radix 2 Sequential Multipliers Left-Shift Version (unsigned): diagram
Radix 2 Sequential Multipliers Right-Shift Version with CSA (unsigned): example, diagram 1, diagram 2, timing 1, timing 2
Lecture 7: Tree and Array Multipliers. [PPT, PDF]
Lecture 6: Multioperand Addition. Modular Addition. [PPT, PDF]
Lecture 5: Floating Point Representations. Rounding. Representation of the Galois Field elements. [PPT, PDF]
Lecture 4: Fixed-Point Representations. Endianness. [PPT, PDF]
Lecture 3: Conditional-Sum Adders and Parallel Prefix Network Adders. FPGA Optimized Adders. [PPT, PDF]
Lecture 2: Carry-Lookahead, Carry-Select, & Hybrid Adders. [PPT, PDF]
Lecture 1: Basic Adders and Counters. Implementation of Adders in FPGAs. [PPT, PDF]
Lecture 0: Objectives, Scope, and Organization of the Course [PPT, PDF]
Posted gradually before a given lecture.
See the course web page from Spring 2013 for slides from the previous year.
Project can be done either individually or
in groups of two students.
The students can choose one of the
following project types:
Recommended Outline of Your Specification
Recommended Outline of Your Presentation
List and Format of Project Deliverables
Recommended Outline of Your Report
Area: Public Key Cryptography
Project 1: Post-quantum public
key-cryptography: McEliece scheme
Project 2: Implementation of RSA using DSP
Project 3: Implementation of RSA based on the Huang et al. architecture for Montgomery multiplication
Area: Coding Theory
Project 4: Reed-Solomon Code for RAID systems
Project 5: Error Correcting Code Encoder and Decoder for Physical Unclonable Functions
R. Maes, A. Van Herrewege, I. Verbauwhede, "PUFKY: A Fully Functional PUF-based Cryptographic Key Generator," Proc. CHES 2012, LNCS 7428, pp. 302-319.
Area: Financial Computations
Project 6: Floating point unit for Decimal64 floating-point format (supporting at least multiplication and addition)
Project 7: Trial Division by Small Primes
Project 8: Pollard's Rho Method of Factoring
Area: FPGA-optimized Arithmetic Units
Project 9: FPGA-optimized Adders and Modular Adders for Long Integers
H. Nguyen, B. Pasca, and T. Preusser, "FPGA-specific arithmetic optimizations of short-latency adders," in 2011 International Conference on Field Programmable Logic and Applications (FPL), 2011, pp. 232–237.
Project 10: Comparative analysis of multi-precision arithmetic libraries for public key cryptography
Project 11: Comparative analysis of DSP units of Xilinx, Altera, and Microsemi FPGAs
Project 12: Comparative analysis of CORDIC-based architectures for Direct Digital Frequency Synthesizer (DDFS)
S.A. Khan, Digital Design of Signal Processing Systems: A Practical Approach, Wiley 2011. Chapter 12: CORDIC-based DDFS Architectures.
Project 13: Comparative analysis of hardware architectures for Fast Fourier Transform
S.A. Khan, Digital Design of Signal Processing Systems: A Practical Approach, Wiley 2011, Chapters 8.5.3-8.5.5, 8.6.
Project 14: Comparative analysis of fast exponentiation algorithms
Homework 4 - due Monday, March 17, 11:59pm; solutions to bonus problems can be submitted by Sunday, March 23, 11:59pm
Homework 3 Bonus - due Saturday, March 1, 11:59pm
Homework 3 - due Wednesday, February 26, 4:30pm; please use the following Answer Sheets
Homework 2 Bonus - due Sunday, February 16, 11:59pm
- due Saturday, February 15, 11:59pm; please use the following Answer Sheets
- due Wednesday, February 5, 4:30pm (at the beginning of the class);
solutions to bonus problems can be submitted by Saturday, February 8,
Posted gradually about a week before a given assignment is due.
See the course web page from Spring 2013 for homework assignment from the previous year.
OpenCores Coding Guidelines
vhdl.org - HDL Resources of EDA Industry Working Groups
ECE 645: Spring 2013, Spring
ECE 545: Fall 2013, Fall 2012
ECE 448: Spring 2013, Spring 2012
DISCLAIMER: The exams from previous years are not representative of the material covered in class this semester, and may include questions you are not required to know solutions to, and omit material covered in class this year.
Midterm Exam from Spring 2013
Midterm Exam from Spring 2012 - solutions
Midterm Exam from Spring 2011
Midterm Exam from Spring 2010 - solutions
Midterm Exam from Spring 2009 - solutions
Midterm Exam 1 from Spring 2007 - solutions
Midterm Exam 1 from Spring 2005 - solutions
Practice Midterm Exam from Spring 2005
Midterm Exam 1 from Spring 2004 - solutions
Practice Midterm Exam from Spring 2004
Midterm Exam 1 from Spring 2002 - solutions
Midterm Exam 1 from Spring 2000
Final Exam from Spring 2013
Final Exam from Spring 2012
Final Exam from Spring 2011
Final Exam from Spring 2010 Solutions: Problem 1, Problem 2, Problem 3, Problem 5
Final Exam from Spring 2009
Midterm Exam 2 from Spring 2007
Midterm Exam 2 from Spring 2006
Midterm Exam 2 from Spring 2005