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Error Coding for Arithmetic Processors provides an understanding of arithmetically invariant codes as a primary technique of fault-tolerant computing by discussing the progress in arithmetic coding theory. The book provides an introduction to arithmetic error code, single-error detection, and long-distance codes. It also discusses algebraic structures, linear congruences, and residues. Organized into eight chapters, this volume begins with an overview of the mathematical background in number theory, algebra, and error control techniques. It then explains the basic mathematical models on a register and its number representation system. The reader is also introduced to arithmetic processors, as well as to error control techniques. The text also explores the functional units of a digital computer, including control unit, arithmetic processor, memory unit, program unit, and input/output unit. Students in advanced undergraduate or graduate level courses, researchers, and readers who are interested in applicable knowledge on arithmetic codes will find this book extremely useful.
Chapter 1 Introduction and Background
1.1 Algebraic Structures
1.2 Theory of Divisibility and Congruences
1.3 Registers and Number Representation Systems
Chapter 2 Arithmetic Processors and Error Control Preliminaries
2.1 Arithmetic Processors and Digital Computers
2.2 Nature and Origin of Errors in AP's
2.3 Error Control Techniques
Chapter 3 Arithmetic Codes, Their Classes and Fundamentals
3.1 Code Classes
3.2 AN Codes and Single-Error Detection
3.3 Checking an Adder by Separate Codes
3.4 Checking Other Elementary Operations
3.5 Residue Generators
Chapter 4 Single-Error Correction
4.1 AN Codes and Preliminaries
4.2 Higher Radix AN Codes
4.3 Cyclic AN Codes
4.4 More on M(A, 3)
Chapter 5 Error Correction Using Separate Codes
5.1 Biresidue Code
5.2 Error Correction Using Biresidue Codes
5.3 Construction of Separate Codes from Nonseparate Codes
Chapter 6 Large-Distance Codes
6.2 Barrows-Mandelbaum (BM) Codes
6.3 Chien-Hong-Preparata (CHP) Codes
6.4 AN Codes for Composite A = II(2ml - 1)
Chapter 7 Other Arithmetic Codes of Interest
7.1 Systematic Nonseparate Codes
7.2 Burst-Error-Correcting Codes
7.3 Iterative Errors
Chapter 8 Recent Results on Arithmetic Codes and Their Applications
8.1 Polynomial Cyclic Codes and Cyclic AN Codes
8.2 BCH Codes and BCH Bound
8.3 On Bounds for dmin of Cyclic AN Codes
8.4 Majority Decodable Arithmetic Codes
8.5 Self-Checking Processors
- No. of pages:
- © Academic Press 1974
- 28th January 1974
- Academic Press
- eBook ISBN:
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