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Arithmetic and Logic in Computer Systems

Book Description

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.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Dedication
  5. Contents
  6. Preface
  7. List of Figures
  8. List of Tables
  9. About the Author
  10. Chapter 1: Computer Number Systems
    1. 1.1 CONVENTIONAL RADIX NUMBER SYSTEM
    2. 1.2 CONVERSION OF RADIX NUMBERS
    3. 1.3 REPRESENTATION OF SIGNED NUMBERS
    4. 1.4 SIGNED-DIGIT NUMBER SYSTEM
    5. 1.5 FLOATING-POINT NUMBER REPRESENTATION
    6. 1.6 RESIDUE NUMBER SYSTEM
    7. 1.7 LOGARITHMIC NUMBER SYSTEM
    8. REFERENCES
    9. PROBLEMS
  11. Chapter 2: Addition and Subtraction
    1. 2.1 SINGLE-BIT ADDERS
    2. 2.2 NEGATION
    3. 2.3 SUBTRACTION THROUGH ADDITION
    4. 2.4 OVERFLOW
    5. 2.5 RIPPLE CARRY ADDERS
    6. REFERENCES
    7. PROBLEMS
  12. Chapter 3: High-Speed Adder
    1. 3.1 CONDITIONAL-SUM ADDITION
    2. 3.2 CARRY-COMPLETION SENSING ADDITION
    3. 3.3 CARRY-LOOKAHEAD ADDITION (CLA)
    4. 3.4 CARRY-SAVE ADDERS (CSA)
    5. 3.5 BIT-PARTITIONED MULTIPLE ADDITION
    6. REFERENCES
    7. PROBLEMS
  13. Chapter 4: Sequential Multiplication
    1. 4.1 ADD-AND-SHIFT APPROACH
    2. 4.2 INDIRECT MULTIPLICATION SCHEMES
    3. 4.3 ROBERTSON'S SIGNED NUMBER MULTIPLICATION
    4. 4.4 RECODING TECHNIQUE
    5. REFERENCES
    6. PROBLEMS
  14. Chapter 5: Parallel Multiplication
    1. 5.1 WALLACE TREES
    2. 5.2 UNSIGNED ARRAY MULTIPLIER
    3. 5.3 TWO'S COMPLEMENT ARRAY MULTIPLIER
    4. 5.4 MODULAR STRUCTURE OF LARGE MULTIPLIER
    5. REFERENCES
    6. PROBLEMS
  15. Chapter 6: Sequential Division
    1. 6.1 SUBTRACT-AND-SHIFT APPROACH
    2. 6.2 BINARY RESTORING DIVISION
    3. 6.3 BINARY NON-RESTORING DIVISION
    4. 6.4 HIGH-RADIX DIVISION
    5. 6.5 CONVERGENCE DIVISION
    6. 6.6 DIVISION BY DIVISOR RECIPROCATION
    7. REFERENCES
    8. PROBLEMS
  16. Chapter 7: Fast Array Dividers
    1. 7.1 RESTORING CELLULAR ARRAY DIVIDER
    2. 7.2 NON-RESTORING CELLULAR ARRAY DIVIDER
    3. 7.3 CARRY-LOOKAHEAD CELLULAR ARRAY DIVIDER
    4. REFERENCES
    5. PROBLEMS
  17. Chapter 8: Floating Point Operations
    1. 8.1 FLOATING POINT ADDITION/SUBTRACTION
    2. 8.2 FLOATING POINT MULTIPLICATION
    3. 8.3 FLOATING POINT DIVISION
    4. 8.4 ROUNDING
    5. 8.5 EXTRA BITS
    6. REFERENCES
    7. PROBLEMS
  18. Chapter 9: Residue Number Operations
    1. 9.1 RNS ADDITION, SUBTRACTION AND MULTIPLICATION
    2. 9.2 NUMBER COMPARISON AND OVERFLOW DETECTION
    3. 9.3 DIVISION ALGORITHM
    4. REFERENCES
    5. PROBLEMS
  19. Chapter 10: Operations through Logarithms
    1. 10.1 MULTIPLICATION AND ADDITION IN LOGARITHMIC SYSTEMS
    2. 10.2 ADDITION AND SUBTRACTION IN LOGARITHMIC SYSTEMS
    3. 10.3 REALIZING THE APPROXIMATION
    4. REFERENCES
    5. PROBLEMS
  20. Chapter 11: Signed-Digit Number Operations
    1. 11.1 CHARACTERISTICS OF SD NUMBERS
    2. 11.2 TOTALLY PARALLEL ADDITION/SUBTRACTION
    3. 11.3 REQUIRED AND ALLOWED VALUES
    4. 11.4 MULTIPLICATION AND DIVISION
    5. REFERENCES
    6. PROBLEMS
  21. Index