EEC 278: Computer Arithmetic

Spring 2001

Prof. Vojin G. Oklobdzija

vojin@ece.ucdavis.edu
Telephone: 752-5634
Office Hours: Tu-Thr 4:00-5:00, and by appointment via e-mail

 

Course Description:

This course addresses selected topics in logic design of arithmetic units for high-performance and low-power systems. In the area of fast VLSI Arithmetic this course will be investigating the relationship between the algorithms and technology, i.e. how efficiently do algorithms map into the specifics of the technology applied.  The knowledge of this relationship enables one to properly select and modify an algorithm so that it would result in the most efficient implementation.

 

Project:

The course carry a project which may require the use of CAD tools (Cadence, H-Spice, Synopsys). It is possible to carry the project to implementation as an extension of this course (thesis project). The project is determined at the beginning of the course. The goal of this project is to provide a possible MSc thesis to result in a publication, or provide a learning research experience.
 

Grading:

Project : 50%  Exams: 50%
 

This short course is divided into five sections of study. Outline is as follows:
 

I.             Introduction and Number Representation:

II.          Basic Arithmetic Algorithms:

III.       Implementation of Addition:

IV.        Multiplication:

V.           Division:

VI.        Square Root:

 


Prerequisite: BSEE or coursework / experience in logic and circuit design 
 

Text:

1. V.G. Oklobdzija,  ”Class Notes and Handouts", April, 2001.

2. Design of High-Performance Microprocessor Circuits ( chapter 10)
edited by Anantha Chandrakasan, MIT, William Bowhill, Compaq Computer
2001;Hardcover;2001;ISBN 0-7803-6001-X; Product No.: PC5836-TBR

Recommended Text:

3. K. Hwang, “Computer Arithmetic, Principles, Architecture, and Design”, New York, NY: John Wiley & Sons, 1979

 

Computer Arithmetic Books

·           J. J. F. Cavanagh
Digital Computer Arithmetic
New York, NY: McGraw-Hill, 1984

·           J. B. Gosling
Design of Arithmetic Units for Digital Computers
New York, NY: Springer-Verlag, 1980

·           K. Hwang
Computer Arithmetic, Principles, Architecture, and Design
New York, NY: John Wiley & Sons, 1979

·           I. Koren
Computer Arithmetic Algorithms
Englewood Cliffs, NJ: Prentice-Hall, 1993

·           U. W. Kulisch and W. L. Miranker
Computer Arithmetic in Theory and Practice
New York, NY: Academic Press, 1981

·           J. H. McClellan and C. M. Rader
Number Theory in Digital Signal Processing
Englewood Cliffs, NJ: Prentice-Hall, 1979

·           A. R. Omondi
Computer Arithmetic Systems: Algorithms, Architecture and Implementations
New York, NY: Prentice-Hall, 1994

·           R. K. Richards
Arithmetic Operations in Digital Computers
Princeton, NJ: D. Van Nostrand, 1955

·           H. Schmid
Decimal Computation
Malabar, FL: Robert E. Krieger, 1983

·           N. R. Scott
Computer Number Systems and Arithmetic
Englewood Cliffs, NJ: Prentice-Hall, 1985

·           M. A. Soderstrand, W. K. Jenkins, G. A. Jullien, and F. J. Taylor
Residue Arithmetic: Modern Applications in Digital Signal Processing
New York, NY: IEEE Press, 1986

·           E. E. Swartzlander
Computer Arithmetic, Volumes I and II
Los Alamitos, CA: IEEE Computer Society Press, 1990

·           N. S. Szabo and R. I. Tanaka
Residue Arithmetic and its Applications to Computer Technology
New York, NY: McGraw-Hill, 1967

·           C. Ullrich
Computer Arithmetic and Self-Validating Numerical Methods
New York, NY: Academic Press, 1990

·           P. J. L. Wallis
Improving Floating-Point Programming
New York, NY: John Wiley & Sons, 1990

·           S. Waser and M. J. Flynn
Introduction to Arithmetic for Digital System Designers
New York, NY: Holt, Rinehart and Winston, 1982

Computer Arithmetic Proceedings

·           Proceedings of 13th Symposium on Computer Arithmetic
T. Lang, J.-M. Muller, and N. Takagi (Editors),
Asilomar, California, July 6-9, 1997. IEEE Computer Society Press.

·           Proceedings of 12th Symposium on Computer Arithmetic
L S. Knowles and W. H. McAllister (Editors),
Bath, England, July 19 - 21, 1995. IEEE Computer Society Press.

·           Proceedings of 11th Symposium on Computer Arithmetic
E. Swartzlander, Jr., M. J. Irwin, and G. Jullien (Editors),
Windsor, Ontario, June 29 - July 2, 1993. IEEE Computer Society Press.

·           Proceedings of 10th Symposium on Computer Arithmetic
P. Kornerup and D. W. Matula (Editors),
Grenoble, France, June 26 - 28, 1991. IEEE Computer Society Press.

·           Proceedings of 9th Symposium on Computer Arithmetic
M. D. Ercegovac and E. Swartzlander (Editors),
Santa Monica, California, September 6 - 8, 1989. IEEE Computer Society Press.

·           Proceedings of 8th Symposium on Computer Arithmetic
M. J. Irwin and R. Stefanelli (Editors),
Como, Italy, May 19 - 21, 1987. IEEE Computer Society Press.

·           Proceedings of 7th Symposium on Computer Arithmetic
Kai Hwang, Editor

University of Illinois, Urbana, Illinois, June4-6, 1985.

·           Proceedings of 6th Symposium on Computer Arithmetic
Aarhus, Denmark, June 20 - 22, 1983.

·           Proceedings of 5th Symposium on Computer Arithmetic
Ann Arbor, Michigan, May 18 - 19, 1981.

·           Proceedings of 4th Symposium on Computer Arithmetic
Santa Monica, California, October 25 - 27, 1978.

·           Proceedings of 3th Symposium on Computer Arithmetic
Dullas, Texas, 1975.

·           Proceedings of 2nd Symposium on Computer Arithmetic
Maryland, 1972

·           Proceedings of 1st Symposium on Computer Arithmetic
Minneapolis, Minnesota, 1969