Computer Arithmetic Algorithms and Implementations

This chapter first introduces two types of the binary representations: unsigned number (absolute) and 2's complement representation for signed integers. It then describes the binary addition and subtraction algorithms and their implementations in Verilog HDL. A carry‐lookahead adder is also des...

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Bibliographic Details
Published in:Computer Principles and Design in Verilog HDL pp. 63 - 110
Main Authors: Li, Yamin, Tsinghua University Press
Format: Book Chapter
Language:English
Published: Singapore Wiley 2015
John Wiley & Sons, Incorporated
John Wiley & Sons, Ltd
Subjects:
binary addition algorithms
binary division algorithms
binary multiplication algorithms
binary square root algorithms
binary subtraction algorithms
carry‐lookahead adder
Verilog HDL
Wallace tree
ISBN:1118841093, 9781118841099
Online Access:Get full text
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Summary:This chapter first introduces two types of the binary representations: unsigned number (absolute) and 2's complement representation for signed integers. It then describes the binary addition and subtraction algorithms and their implementations in Verilog HDL. A carry‐lookahead adder is also described. Next, the chapter discusses unsigned and signed binary multiplication algorithms and their implementations in Verilog HDL. The Wallace tree, which is a high‐speed multiplication circuit, is also introduced. It then introduces unsigned binary division algorithms, including the restoring algorithm, the non‐restoring algorithm, the Goldschmidt algorithm, and the Newton‐Raphson algorithm. The Verilog HDL codes that implement these algorithms and their simulation waveforms are also given. The chapter also introduces binary square root algorithms, including the restoring algorithm, the nonrestoring algorithm, the Goldschmidt algorithm, and the Newton‐Raphson algorithm. The Verilog HDL codes that implement these algorithms and their simulation waveforms are also given.
ISBN:1118841093
9781118841099
DOI:10.1002/9781118841105.ch3