Computer Arithmetic: Algorithms and Hardware Designs, 2nd Edition

Ideal for graduate and senior undergraduate courses in computer arithmetic and advanced digital design, Computer Arithmetic: Algorithms and Hardware Designs, Second Edition, provides a balanced, comprehensive treatment of computer arithmetic. It covers topics in arithmetic unit design and circuit implementation that complement the architectural and algorithmic speedup techniques used in high-performance computer architecture and parallel processing. Using a unified and consistent framework, the text begins with number representation and proceeds through basic arithmetic operations, floating-point arithmetic, and function evaluation methods. Later chapters cover broad design and implementation topics-including techniques for high-throughput, low-power, fault-tolerant, and reconfigurable arithmetic. An appendix provides a historical view of the field and speculates on its future.

An indispensable resource for instruction, professional development, and research, Computer Arithmetic: Algorithms and Hardware Designs, Second Edition, combines broad coverage of the underlying theories of computer arithmetic with numerous examples of practical designs, worked-out examples, and a large collection of meaningful problems. This second edition includes a new chapter on reconfigurable arithmetic, in order to address the fact that arithmetic functions are increasingly being implemented on field-programmable gate arrays (FPGAs) and FPGA-like configurable devices. Updated and thoroughly revised, the book offers new and expanded coverage of saturating adders and multipliers, truncated multipliers, fused multiply-add units, overlapped quotient digit selection, bipartite and multipartite tables, reversible logic, dot notation, modular arithmetic, Montgomery modular reduction, division by constants, IEEE floating-point standard formats, and interval arithmetic.

Features:

* Divided into 28 lecture-size chapters
* Emphasizes both the underlying theories of computer arithmetic and actual hardware designs
* Carefully links computer arithmetic to other subfields of computer engineering
* Includes 717 end-of-chapter problems ranging in complexity from simple exercises to mini-projects
* Incorporates many examples of practical designs
* Uses consistent standardized notation throughout
* Instructor’s manual includes solutions to text problems
* An author-maintained website http://www.ece.ucsb.edu/~parhami/text_comp_arit.htm contains instructor resources, including complete lecture slides

Table of Contents

PART I NUMBER REPRESENTATION
Chapter 1 Numbers and Arithmetic
Chapter 2 Representing Signed Numbers
Chapter 3 Redundant Number Systems
Chapter 4 Residue Number Systems

PART II ADDITION/SUBTRACTION
Chapter 5 Basic Addition and Counting
Chapter 6 Carry-Lookahead Adders
Chapter 7 Variations in Fast Adders
Chapter 8 Multioperand Addition

PART III MULTIPLICATION
Chapter 9 Basic Multiplication Schemes
Chapter 10 High-Radix Multipliers
Chapter 11 Tree and Array Multipliers
Chapter 12 Variations in Multipliers

PART IV DIVISION
Chapter 13 Basic Division Schemes
Chapter 14 High-Radix Dividers
Chapter 15 Variations in Dividers
Chapter 16 Division by Convergence

PART V REAL ARITHMETIC
Chapter 17 Floating-Point Representations
Chapter 18 Floating-Point Operations
Chapter 19 Errors and Error Control
Chapter 20 Precise and Certifiable Arithmetic

PART VI FUNCTION EVALUATION
Chapter 21 Square-Rooting Methods
Chapter 22 The CORDIC Algorithms
Chapter 23 Variations in Function Evaluation
Chapter 24 Arithmetic by Table Lookup

PART VII IMPLEMENTATION TOPICS
Chapter 25 High-Throughput Arithmetic
Chapter 26 Low-Power Arithmetic
Chapter 27 Fault-Tolerant Arithmetic
Chapter 28 Reconfigurable Arithmetic

Appendix: Past, Present, and Future