- Title Page
- Copyright Page
- Dedication Page
- Contents
- Foreword
- Preface
- Chapter 1. Introduction
- Chapter 2. Basics
- 2–1 Manipulating Rightmost Bits
- 2–2 Addition Combined with Logical Operations
- 2–3 Inequalities among Logical and Arithmetic Expressions
- 2–4 Absolute Value Function
- 2–5 Average of Two Integers
- 2–6 Sign Extension
- 2–7 Shift Right Signed from Unsigned
- 2–8 Sign Function
- 2–9 Three-Valued Compare Function
- 2–10 Transfer of Sign Function
- 2–11 Decoding a “Zero Means 2**n” Field
- 2–12 Comparison Predicates
- 2–13 Overflow Detection
- 2–14 Condition Code Result of Add, Subtract, and Multiply
- 2–15 Rotate Shifts
- 2–16 Double-Length Add/Subtract
- 2–17 Double-Length Shifts
- 2–18 Multibyte Add, Subtract, Absolute Value
- 2–19 Doz, Max, Min
- 2–20 Exchanging Registers
- 2–21 Alternating among Two or More Values
- 2–22 A Boolean Decomposition Formula
- 2–23 Implementing Instructions for All 16 Binary Boolean Operations
- Chapter 3. Power-of-2 Boundaries
- Chapter 4. Arithmetic Bounds
- Chapter 5. Counting Bits
- Chapter 6. Searching Words
- Chapter 7. Rearranging Bits and Bytes
- 7–1 Reversing Bits and Bytes
- 7–2 Shuffling Bits
- 7–3 Transposing a Bit Matrix
- 7–4 Compress, or Generalized Extract
- 7–5 Expand, or Generalized Insert
- 7–6 Hardware Algorithms for Compress and Expand
- 7–7 General Permutations, Sheep and Goats Operation
- 7–8 Rearrangements and Index Transformations
- 7–9 An LRU Algorithm
- Chapter 8. Multiplication
- Chapter 9. Integer Division
- Chapter 10. Integer Division By Constants
- 10–1 Signed Division by a Known Power of 2
- 10–2 Signed Remainder from Division by a Known Power of 2
- 10–3 Signed Division and Remainder by Non-Powers of 2
- 10–4 Signed Division by Divisors ≥ 2
- 10–5 Signed Division by Divisors ≤ –2
- 10–6 Incorporation into a Compiler
- 10–7 Miscellaneous Topics
- 10–8 Unsigned Division
- 10–9 Unsigned Division by Divisors ≥ 1
- 10–10 Incorporation into a Compiler (Unsigned)
- 10–11 Miscellaneous Topics (Unsigned)
- 10–12 Applicability to Modulus and Floor Division
- 10–13 Similar Methods
- 10–14 Sample Magic Numbers
- 10–15 Simple Code in Python
- 10–16 Exact Division by Constants
- 10–17 Test for Zero Remainder after Division by a Constant
- 10–18 Methods Not Using Multiply High
- 10-19 Remainder by Summing Digits
- 10–20 Remainder by Multiplication and Shifting Right
- 10–21 Converting to Exact Division
- 10–22 A Timing Test
- 10–23 A Circuit for Dividing by 3
- Chapter 11. Some Elementary Functions
- Chapter 12. Unusual Bases for Number Systems
- Chapter 13. Gray Code
- Chapter 14. Cyclic Redundancy Check
- Chapter 15. Error-Correcting Codes
- Chapter 16. Hilbert’s Curve
- 16–1 A Recursive Algorithm for Generating the Hilbert Curve
- 16–2 Coordinates from Distance along the Hilbert Curve
- 16–3 Distance from Coordinates on the Hilbert Curve
- 16–4 Incrementing the Coordinates on the Hilbert Curve
- 16–5 Non-Recursive Generating Algorithms
- 16–6 Other Space-Filling Curves
- 16–7 Applications
- Chapter 17. Floating-Point
- Chapter 18. Formulas For Primes
- Answers To Exercises
- Chapter 1: Introduction
- Chapter 2: Basics
- Chapter 3: Power-of-2 Boundaries
- Chapter 4: Arithmetic Bounds
- Chapter 5: Counting Bits
- Chapter 6: Searching Words
- Chapter 7: Rearranging Bits and Bytes
- Chapter 8: Multiplication
- Chapter 9: Integer Division
- Chapter 10: Integer Division by Constants
- Chapter 11: Some Elementary Functions
- Chapter 12: Unusual Bases for Number Systems
- Chapter 13: Gray Code
- Chapter 14: Cyclic Redundancy Check
- Chapter 15: Error-Correcting Codes
- Chapter 16: Hilbert’s Curve
- Chapter 17: Floating-Point
- Chapter 18: Formulas for Primes
- Appendix A. Arithmetic Tables for A 4-Bit Machine
- Appendix B. Newton’s Method
- Appendix C. A Gallery of Graphs of Discrete Functions
- Bibliography
- Index
- Footnotes
To Joseph W. Gauld, my high school algebra teacher, for sparking in me a delight in the simple things in mathematics
-
No Comment
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.