COE 586 (3-0-3)

Computer Arithmetic


Catalog Description

Fixed point arithmetic: addition, subtraction, multiplication, divsion, fixed point ALUs. Floating point arithmetic: normalization, rounding, addition, subtraction, multiplication, divsion, floating point ALU. Modeling of Arithmetic Processors. Elementary functions. Nonconventional Number Systems.




       1.         Fixed-Point Number System (Overview, Classification Unsigned/Signed)


       2.         Nonconventional Number Systems (Redundant Signed Digit Number System and Residue Number System(RNS)).


       3.         Fixed-Point Addition/Subtraction (Basic Adder configuration, Carry Lookahead Adders, Conditional Sum adder, Manchester Carry Chains, Carry Completion Self-Timed Adders, Carry Select Adder,Carry Skip Adders, and Pyramid Adders)


       4.         Multioperand Addition(Operands bit arrays, Reduction structures. Algorithms and implementations)


       5.         Fixed Point Multipliers (Basic Algorithms, Fast Multiplication Techniques, Evaluation of Polynomials, Exponentiation, Parallel and Table lookup Multipliers, Modulo Multipliers)


       6.         Fixed Point Division (Restoring & Nonrestoring Division, Binary and High-Radix Division Algorithms, Design & Implementation of dividers, Division by convergenece, Square root)


       7.         Computation of elementary functions- The CORDIC Algorithms (Trigonometric and Hyperbolic functions, Basic theory, Rotation, Basic Iterations, Hardware and the Generalized CORDIC).


       8.         Digit-Serial Arithmetic (LSDF , MSDF / online)


       9.         Floating-Point Number System (Overview, Normalization, Overflow/Underflow,  Number Representation, Floating point operations, Error analysis)


     10.       Implementation of Floating-Point Operations (Rounding, Addition & Subtraction, Multiplication & Division)



Reference Books

1.      Israel Koren, “Computer Arithmetic algorithms,” second edition, A. K. Peters Ltd. 2002

2.      Digital Arithmetic by M. D. Ercegovac and T. Lang, Morgan and Kaufmann, 2004

3.      Behrooz Parhami, “Computer Arithmetics: Algorithms and Hardware Design”, Oxford University Press, 2000.

Grading Policy

Option 1

Option 2

·         Homework Assignments ..   15%

·         Midterm Exam                    20%

·         Project                               20%

·         Paper Presentations             15%

·         Quizzes                              10%

·         Final Exam                         20%

·        Homework Assignments .   15%

·        Midterm Exam                  20%

·        Project / Paper Writing      40%

·         Paper Presentations           15%

·         Quizzes                            10%