Arithmetic and Logic in Computer Systems

✍ Scribed by Mi Lu

• Publisher: Wiley-Interscience
• Year: 2004
• Tongue: English
• Leaves: 269
• Edition: 1
• Category: Library

✦ Synopsis

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

Arithmetic and Logic in Computer Systems
Contents
Preface
List of Figures
List of Tables
About the Author
Computer Number Systems
1.1 CONVENTIONAL RADIX NUMBER SYSTEM
1.2 CONVERSION OF RADIX NUMBERS
1.3 REPRESENTATIONOF SIGNED NUMBERS
1.3.1 Sign-Magnitude
1.3.2 DiminishedRadix Complement
1.3.3 Radix Complement
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
Addition and Subtraction
2.1 SINGLE-BIT ADDERS
2.1.1 Logical Devices
2.1.2 Single-Bit Half-Adderand Full-Adders
2.2 NEGATION


2.3 SUBTRACTIONTHROUGH ADDITION
2.4 OVERFLOW
2.5 RIPPLE CARRY ADDERS


2.5.3 Sign-MagnitudeAddition
REFERENCES
PROBLEMS
High-speed Adder
3.1 CONDITIONAL-SUM ADDITION
3.2 CARRY-COMPLETION SENSING ADDITION
3.3 CARRY-LOOKAHEAD ADDITION (CLA)
3.3.1 Carry-Lookahead Adder
3.3.2 Block Carry Lookahead Adder
3.4 CARRY-SAVE ADDERS (CSA)
3.5 BIT-PARTITIONED MULTIPLE ADDITION
REFERENCES
PROBLEMS
Sequential Multiplication
4.1 ADD-AND-SHIFT APPROACH
4.2 INDIRECT MULTIPLICATIONSCHEMES
4.2.1 Unsigned Number Multiplication
4.2.2 Sign-MagnitudeNumber Multiplication



4.4 RECODINGTECHNIQUE
4.4.1 Non-overlappedMultiple Bit Scanning
4.4.2 Overlapped MultipleBit Scanning

4.4.4 Canonical Multiplier Recoding
REFERENCES
PROBLEMS
Parallel Multiplication
5.1 WALLACE TREES
5.2 UNSIGNEDARRAY MULTIPLIER


5.3.2 Pezaris Two’s Complement Multipliers
5.4 MODULAR STRUCTURE OF LARGE MULTIPLIER
5.4.1 Modular Structure
5.4.2 Additive Multiply Modules
5.4.3 Programmable Multiply Modules
REFERENCES
PROBLEMS
Sequential Division
6.1 SUBTRACT-AND-SHIFT APPROACH
6.2 BINARY RESTORINGDIVISION
6.3 BINARY NON-RESTORING DIVISION
6.4 HIGH-RADIX DIVISION
6.4.1 High-Radix Non-Restoring Division
6.4.2 SRT Division
6.4.3 Modified SRT Division
6.4.4 Robertson's High-Radix 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
Fast Array Dividers
7.1 RESTORING CELLULAR ARRAY DIVIDER
7.2 NON-RESTORING CELLULAR ARRAY DIVIDER
7.3 CARRY-LOOKAHEAD CELLULAR ARRAY DIVIDER
REFERENCES
PROBLEMS
Floating Point Operations
8.1 FLOATING POINT ADDITION/SUBTRACTION
8.2 FLOATING POINT MULTIPLICATION
8.3 FLOATING POINT DIVISION
8.4 ROUNDING
REFERENCES
PROBLEMS
Residue Number Operations
9.1 RNS ADDITION, SUBTRACTION AND MULTIPLICATION
9.2 NUMBER COMPARISONAND 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 Inverseand the Parity Table
9.3 DIVISION ALGORITHM
9.3.1 Unsigned Number Division
9.3.2 Signed Number Division
REFERENCES
PROBLEMS
Operations through
Operations through Logarithms
10.1 MULTIPLICATIONAND ADDITION IN LOGARITHMICSYSTEMS
10.2 ADDITION AND SUBTRACTIONIN LOGARITHMICSYSTEMS
10.3 REALIZING THE APPROXIMATION
REFERENCES
PROBLEMS
Signed-Digit Number Operations
11.1 CHARACTERISTICS
11.2 TOTALLY PARALLELADDITION/SUBTRACTION
11.3 REQUIRED AND ALLOWED VALUES
11.4 MULTIPLICATIONAND DIVISION
REFERENCES
PROBLEMS
Index
End of Book