# Arithmetic and Logic in Computer Systems / Edition 1

by Mi Lu

ISBN-10: 0471469459

ISBN-13: 9780471469452

Pub. Date: 01/28/2004

Publisher: Wiley

Arithmetic and Logic in Computer Systems provides a useful guide to a fundamental subject of computer science and engineering. Algorithms for performing operations like addition, subtraction, multiplication, and division in digital computer systems are presented, with the goal of explaining the concepts behind the algorithms, rather than addressing any direct

## Overview

Arithmetic and Logic in Computer Systems provides a useful guide to a fundamental subject of computer science and engineering. Algorithms for performing operations like addition, subtraction, multiplication, and division in digital computer systems are presented, with the goal of explaining the concepts behind the algorithms, rather than addressing any direct applications. Alternative methods are examined, and explanations are supplied of the fundamental materials and reasoning behind theories and examples.
No other current books deal with this subject, and the author is a leading authority in the field of computer arithmetic. The text introduces the Conventional Radix Number System and the Signed-Digit Number System, as well as Residue Number System and Logarithmic Number System. This book serves as an essential, up-to-date guide for students of electrical engineering and computer and mathematical sciences, as well as practicing engineers and computer scientists involved in the design, application, and development of computer arithmetic units.

## Product Details

ISBN-13:
9780471469452
Publisher:
Wiley
Publication date:
01/28/2004
Series:
Wiley Series in Microwave and Optical Engineering Series , #169
Edition description:
New Edition
Pages:
246
Product dimensions:
6.46(w) x 9.65(h) x 0.94(d)

## Related Subjects

Preface.

List of Figures.

List of Tables.

1. Computer Number Systems.

1.3 Representation of Signed Numbers.

1.3.1 Sign-Magnitude.

1.4. Signed-Digit Number System.

1.5 Floating-Point Number Representation.

1.5.1 Normalization.

1.5.2 Bias.

1.6 Residue Number System.

1.7 Logarithmic Number System.

References.

Problems.

2.1.1 Logical Devices.

2.2 Negation.

2.2.1 Negation in One's Complement System.

2.2.2 Negation in Two's Complement System.

2.4 Overflow.

References.

Problems.

References.

Problems.

4. Sequential Multiplication.

4.2 Indirect Multiplication Schemes.

4.2.1 Unsigned Number Multiplication.

4.2.2 Sign-Magnitude Number Multiplication.

4.2.3 One's Complement Number Multiplication.

4.2.4 Two's Complement Number Multiplication.

4.3 Robertson's Signed Number Multiplication.

4.4 Recoding Technique.

4.4.1 Non-overlapped Multiple Bit Scanning.

4.4.2 Overlapped Multiple Bit Scanning.

4.4.3 Booth's Algorithm.

4.4.4 Canonical Multiplier Recoding.

References.

Problems.

5. Parallel Multiplication.

5.1 Wallace Trees.

5.2 Unsigned Array Multiplier.

5.3 Two's Complement Array Multiplier.

5.3.1 Baugh-Wooley Two's Complement Multiplier.

5.3.2 Pezaris Two's Complement Multipliers.

5.4 Modular Structure of Large Multiplier.

5.4.1 Modular Structure.

5.4.3 Programmable Multiply Modules.

References.

Problems.

6. Sequential Division.

6.1 Subtract-and-Shift Approach.

6.2 Binary Restoring Division.

6.3 Binary Non-Restoring Division.

6.4.2 SRT Division.

6.4.3 Modified SRT Division.

6.5 Convergence Division.

6.5.1 Convergence Division Methodologies.

6.5.2 Divider Implementing Convergence Division Algorithm.

6.6 Division by Divisor Reciprocation.

References.

Problems.

7. Fast Array Dividers.

7.1 Restoring Cellular Array Divider.

7.2 Non-Restoring Cellular Array Divider.

References.

Problems.

8. Floating Point Operations.

8.2 Floating Point Multiplication.

8.3 Floating Point Division.

8.4 Rounding.

8.5 Extra Bits.

References.

Problems.

9. Residue Number Operations.

9.1 RNS Addition, Subtraction and Multiplication.

9.2 Number Comparison and Overflow Detection.

9.2.1 Unsigned Number Comparison.

9.2.2 Overflow Detection.

9.2.3 Signed Numbers and Their Properties.

9.2.4 Multiplicative Inverse and the Parity Table.

9.3 Division Algorithm.

9.3.1 Unsigned Number Division.

9.3.2 Signed Number Division.

9.3.3 Multiplicative Division Algorithm.

References.

Problems.

10. Operations through Logarithms.

10.1 Multiplication and Addition in Logarithmic Systems.

10.2 Addition and Subtraction in Logarithmic Systems.

10.3 Realizing the Approximation.

References.

Problems.

11. Signed-Digit Number Operations.

11.1 Characteristics of SD Numbers.

11.3 Required and Allowed Values.

11.4 Multiplication and Division.

References.

Problems.

Index.

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