## Computer Arithmetic: Algorithms and Hardware DesignsIdeal 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 |

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### Contents

NUMBER REPRESENTATION | 1 |

Representing Signed Numbers | 25 |

Redundant Number Systems | 44 |

Copyright | |

27 other sections not shown

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### Common terms and phrases

2's-complement adder adding addition algorithm allow applications approximate arithmetic array assuming binary bits block carry carry-lookahead carry-save Chapter circuit combined Compare complement complexity Computer Arithmetic Computers Consider constant convert cost counter cycle decimal delay depicted derived determine digit set discussed divider division efficient encoding error example Figure final floating-point format four fractional function gate given hardware IEEE Trans implementation inputs integer k-bit leads levels logic method multiplier needed negative Note number system obtained operands operations output parallel partial product partial remainder performed position possible preceding precision prefix problem propagation quotient digit radix radix-4 range recoding reduce redundant Repeat representation represented residue respect result rounding scheme selection shift Show signals simple speed step subtraction tree units unsigned values width