Mi Lu received her MS and PhD in electrical engineering from Rice University, Houston. She joined the Department of Electrical Engineering at Texas A&M University in 1987 and is currently a professor. Her research interests include computer arithmetic, parallel computing, parallel computer architectures, VLSI algorithms, and computer networks. She has published over one hundred technical papers, and has served as associate editor of the Journal of Computing and Information and the Information Sciences Journal. She was conference chairperson of the Fifth, Sixth, and Seventh International Conferences on Computer Science and Informatics. She served on the panel of the National Science Foundation, the panel of the IEEE Workshop on Imprecise and Approximate Computation, and many conference program committees. She is the chairperson of sixty research advisory committees for masters and doctoral students. Dr. Lu is a registered professional engineer and a senior member of the IEEE. She has been recognized in Who’s Who in America.
Summary
A practical introduction to fundamentals of computer arithmetic.
Computer arithmetic is one of the foundations of computer science and engineering. Designed as both a practical
reference for engineers and computer scientists and an introductory text for students of electrical engineering
and the computer and mathematical sciences, Arithmetic and Logic in Computer Systems describes the various algorithms
and implementations in computer arithmetic and explains the fundamental principles that guide them.
Focusing on promoting an understanding of the concepts, Professor Mi Lu addresses:
Number representations, including the Conventional Radix and
Signed-Digit Number Systems as well as Floating Point, Residue, and Logarithmic Number Systems
Ripple Carry Adders and high-speed adders
Sequential multiplication, parallel multiplication, sequential division, and fast array dividers
Floating point operations, Residue Number operations, and operations through logarithms
To assist the reader, alternative methods are examined and thorough explanations of the material are supplied,
along with discussions of the reasoning behind the theory. Ample examples and problems help the reader master the
concepts.
Table of Contents
Preface.
List of Figures.
List of Tables.
About the Author.
1. Computer Number Systems.
1.1 Conventional Radix Number System.
1.2 Conversion of Radix Numbers.
1.3 Representation of Signed Numbers.
1.3.1 Sign-Magnitude.
1.3.2 Diminished Radix Complement.
1.3.3 Radix Complement.
1.4. Signed-Digit Number System.
1.5 Floating-Point Number Representation.
1.5.1 Normalization.
1.5.2 Bias.
1.6 Residue Number System.
1.7 Logarithmic Number System.
References.
Problems.
8.1 Floating Point Addition/Subtraction.
8.2 Floating Point Multiplication.
8.3 Floating Point Division.
8.4 Rounding.
8.5 Extra Bits.
References.
Problems.
9. Residue Number Operations.
9.1 RNS Addition, Subtraction and Multiplication.
9.2 Number Comparison and Overflow Detection.
9.2.1 Unsigned Number Comparison.
9.2.2 Overflow Detection.
9.2.3 Signed Numbers and Their Properties.
9.2.4 Multiplicative Inverse and the Parity Table.
9.3 Division Algorithm.
9.3.1 Unsigned Number Division.
9.3.2 Signed Number Division.
9.3.3 Multiplicative Division Algorithm.
References.
Problems.
10. Operations through Logarithms.
10.1 Multiplication and Addition in Logarithmic Systems.
10.2 Addition and Subtraction in Logarithmic Systems.
10.3 Realizing the Approximation.
References.
Problems.
11. Signed-Digit Number Operations.
11.1 Characteristics of SD Numbers.
11.2 Totally Parallel Addition/Subtraction.
11.3 Required and Allowed Values.
11.4 Multiplication and Division.
References.
Problems.
