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# Arithmetic and Logic in Computer Systems. Wiley Series in Microwave and Optical Engineering

• ID: 2181185
• Book
• 246 Pages
• John Wiley and Sons Ltd
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A practical introduction to fundamentals of computer arithmetic

Computer arithmetic is one of the foundations of computer science and engineering. Designed as both a practical reference for engineers and computer scientists and an introductory text for students of electrical engineering and the computer and mathematical sciences, Arithmetic and Logic in Computer Systems describes the various algorithms and implementations in computer arithmetic and explains the fundamental principles that guide them.

Focusing on promoting an understanding of the concepts, Professor Mi Lu addresses:

• Number representations, including the Conventional Radix and
• Signed–Digit Number Systems as well as Floating Point, Residue, and Logarithmic Number Systems
• Sequential multiplication, parallel multiplication, sequential division, and fast array dividers
• Floating point operations, Residue Number operations, and operations through logarithms

To assist the reader, alternative methods are examined and thorough explanations of the material are supplied, along with discussions of the reasoning behind the theory. Ample examples and problems help the reader master the concepts.

Note: Product cover images may vary from those shown
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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.

Note: Product cover images may vary from those shown
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