Computer arithmetic: Key insights

"Computer Arithmetic: Key Insights" is a comprehensive guide that explores the fundamental principles and advanced concepts of computer arithmetic. From numerical representation to algorithms and hardware implementation, this book provides clear explanations, real-world examples, and practical insights. It covers topics such as number systems, arithmetic operations, precision issues, error analysis, parallel algorithms, and hardware implementations. Whether you're a student, researcher, or professional, this invaluable resource equips you with the necessary knowledge to tackle the challenges of modern computing. With its blend of theory and application, "Computer Arithmetic: Key Insights" is a must-have for anyone seeking a deeper understanding of computer arithmetic and its practical implications. Cover Half Title Page Title Page Copyright About the Author Table of Contents List of Figures List of Tables Preface Chapter 1: Introduction to Computer Arithmetic 1.1. Introduction 1.2. Application of Arithmetic 1.3. Semi-morphic Computer Operations 1.4. Computer Arithmetic 1.5. Summary References Chapter 2: Implementation of Arithmetic in Computers 2.1. Introduction 2.2. A Quick Review of Integer Arithmetic Realization 2.3. Introduction and Features of Real Numbers 2.4. Floating-point Numbers 2.5. Subnormal Floating-point Numbers 2.6. Ieee Floating-point Standard 2.7. Additional Arithmetic Features 2.8. Summary References Chapter 3: Decimal Arithmetic 3.1. Introduction 3.2. The Arithmetic Model 3.3. Subnormal Numbers and Underflow 3.4. Contextual Information Represented Abstractly 3.5. Add and Subtract 3.6. Division 3.7. Divide-integer 3.8. Operation Differences 3.9. Design Concepts 3.10. Summary References Chapter 4: Real Arithmetic: Floating Operations 4.1. History 4.2. Desirable Properties 4.3. Floating-point Numbers 4.4. Rounding 4.5. Properties of Arithmetic On Real Numbers 4.6. Floating-Point Addition and Subtraction 4.7. Floating-Point Multiplication 4.8. Floating-Point Fused Multiply-Add 4.9. Floating-Point Division 4.10. Floating-Point Square Root 4.11. Summary References Chapter 5: Addition and Subtraction 5.1. Single-bit Adders 5.2. Contradictions 5.3. Subtraction Through Addition 5.4. Overflow 5.5. Ripple Carry Adders 5.6. High-speed Adders 5.7. Carry-look Ahead Addition 5.8. Carry-save Adders 5.9. Bit-partitioned Multiple Addition 5.10. Summary References Chapter 6: Multiplication 6.1. Add-and-shift Approach 6.2. Indirect Multiplication Schemes 6.3. Robertson’s Signed Number Multiplication 6.4. Recoding Technique 6.5. Wallace Trees 6.6. Unsigned Array Multiplier 6.7. Two’s Complement Array Multiplier 6.8. Modular Structure of Large Multiplier 6.9. Summary References Chapter 7: Division 7.1. Subtract-and-shift Approach 7.2. Binary Restoring Division 7.3. Binary Non-restoring Division 7.4. High-radix Division 7.5. Convergence Division 7.6. Division by Divisor Reciprocation 7.7. Fast Array Dividers 7.8. Non-restoring Cellular Array Divider 7.9. Carry-lookahead Cellular Array Divider 7.10. Summary References Chapter 8: The FFT and Modular Arithmetic 8.1. Representation 8.2. Addition and Subtraction 8.3. Multiplication 8.4. Division and Inversion 8.5. Exponentiation 8.6. Chinese Remainder Theorem 8.7. Summary References Index Back Cover