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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
Contents
Table of Contents
Preface
Part I: NUMBER REPRESENTATION
1. Numbers and Arithmetic
2. Representing Signed Numbers
3. Redundant Number Systems
4. Residue Number Systems
Part II: ADDITION/SUBTRACTION
5. Basic Addition and Counting
6. Carry - Lookahead Adders
7. Variations in Fast Adders
8. Multioperand Addition
Part III: MULTIPLICATION
9. Basic Multiplication Schemes
10. High - Radix Multipliers
11. Tree and Array Multipliers
12. Variations in Multipliers
Part IV: DIVISION
13. Basic Division Schemes
14. High - Radix Dividers
15. Variations in Dividers
16. Division by Convergence
PART V: REAL ARITHMETIC
17. Floating - Point Representations
18. Floating - Point Operations
19. Errors and Error Control
20. Precise and Certifiable Arithmetic
PART VI: FUNCTION EVALUATION
21. Square - Rooting Methods
22. The CORDIC Algorithms
23. Variations in Function Evaluation
24. Arithmetic by Table Lookup
25. High - Throughput Arithmetic
PART VII: IMPLEMENTATION TOPICS
26. Low - Power Arithmetic
27. Fault - Tolerant Arithmetic
28. Reconfigurable Arithmetic
APPENDIX: PAST, PRESENT, AND FUTURE
A.1 Historical Perspective
A.2 Early High - Performance Machine
A.3 Deeply Pipelined Vector Machines
A.4 The DSP Revolution
A.5 Supercomputers on Our Laps
A.6 Trends Outlook and Resources
