Computer Arithmetic: Algorithms and Hardware Designs (The ^AOxford Series in Electrical and Computer Engineering)
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
Why Read This Book
You should read this book if you want a unified, rigorous treatment of the algorithms behind integer and floating‑point arithmetic together with practical guidance for implementing them in hardware. You will learn not only classical adders, multipliers, dividers, and floating‑point units, but also high‑throughput, low‑power, fault‑tolerant and reconfigurable implementation techniques that map directly to FPGAs and ASICs.
Who Will Benefit
Ideal for senior undergraduates, graduate students, and practicing digital/hardware designers who need to design, analyze, or implement high‑performance arithmetic units and FPGA/ASIC datapaths.
Level: Advanced — Prerequisites: Basic digital logic and circuit design, familiarity with number systems, elementary algorithms and data structures, and an introductory course in computer organization or digital signal processing.
Key Takeaways
- Analyze number representations and quantify tradeoffs between fixed‑ and floating‑point formats.
- Design and optimize a variety of adder, multiplier, and divider architectures for area, latency, and throughput.
- Implement IEEE‑754 compliant floating‑point units and apply rounding, normalization, and exception handling correctly.
- Apply iterative and non‑iterative algorithms (CORDIC, SRT, Newton/Goldschmidt) for efficient function evaluation and division.
- Map arithmetic algorithms to hardware with techniques for pipelining, parallelism, low‑power design, and reconfigurable (FPGA) implementation.
- Evaluate fault‑tolerance, numerical error, and performance tradeoffs to make implementation decisions for real systems.
Topics Covered
- 1. Number Systems and Representations
- 2. Basic Integer Arithmetic: Adders and Subtractors
- 3. Multiplication Algorithms and Hardware
- 4. Division and Reciprocal Algorithms (Restoring, Non‑restoring, SRT, Goldschmidt, Newton)
- 5. Redundant and Signed‑Digit Arithmetic
- 6. Floating‑Point Systems and IEEE‑754
- 7. Floating‑Point Algorithms: Normalization, Rounding, Exceptions
- 8. Function Evaluation: Polynomial Approximation and CORDIC
- 9. High‑Throughput and Low‑Power Implementation Techniques (Pipelining, Parallelism, Retiming)
- 10. Fault‑Tolerance, Testing, and Reliability in Arithmetic Units
- 11. Reconfigurable Computing and FPGA Implementation Issues
- 12. Case Studies, Design Examples and Implementation Notes
- Appendices: Mathematical Background, Error Analysis, Tables
Languages, Platforms & Tools
How It Compares
Covers similar core material as Ercegovac & Lang's Digital Arithmetic but Parhami offers a broader, textbook‑style treatment that links algorithms to implementation, and is more classroom‑oriented than Muller's Handbook of Floating‑Point Arithmetic which is deeper on IEEE‑754 specifics.
