Computer Arithmetics for Nanoelectronics

by Shmerko; Vlad P.

• ISBN13: 9781420066210
• ISBN10: 1420066218
• Format: Hardcover
• Copyright: 2009-02-23
• Publisher: CRC Press

Summary

Employing a refreshingly accessible presentation, this book provides the first introduction to the key multidisciplinary problem of computational nanostructure design viewed from the concept of change. The authors explore the computational paradigms that serve as the basis for the design techniques of computational nanostructures - nanocells and logic networks using connected nanocells. Moving from a physical to a logical level, this material bridges a number of theories. It brings together the highly diverse focuses and experience of specialists in computational nanostructure development. Useful on the practical level, it provides a set of user-friendly guidelines for the basics of nanocircuit design.

Table of Contents

Introduction Computational paradigms for nanocomputing structures

Biological inspiration for computing

Self-assembly Molecular computing devices

Fault tolerance Computing in 3D Multivalued processing

Computational Nanostructures Introduction

Theoretical background Analysis and synthesis

Implementation technologies Predictable technologies

Nanoelectronic networks Switch-based computing structures

Spatial computational nanostructures Binary Arithmetic

Introduction Positional numbers Counting in a positional number system

Basic arithmetic operations in various number systems

Binary arithmetic Radix-complement representations

Conversion of numbers in various radices Overflow

Implementation of binary arithmetic Other binary codes

Further study Residue Arithmetic Introduction Residue arithmetic

Further study Graph-Based Data Structures Introduction Graphs in discrete device and system design

Basic definitions Tree-like graphs and decision trees Voronoi diagrams

Further study Foundation of Boolean Data Structures

Introduction Definition of algebra over the set {0, 1} Boolean functions

Fundamentals of computing Boolean functions Proving the validity of Boolean equations

Gates Local transformations Properties of switching functions

Further study Boolean Data Structures Introduction

Data structure types Relationships between data structures

The truth table K-map Cube data structure Graphical data structure for cube representation

Logic networks Networks of threshold gates Binary decision trees

Decision diagrams Further study Fundamental Expansions

Introduction Shannon expansion Shannon expansion for symmetric

Boolean functions Techniques for computing symmetric functions

The logic Taylor expansion Graphical representation of the fundamental expansions

Further study Arithmetic of the Polynomials Introduction

Algebra of the polynomial forms GF(2) algebra Relationship between standard

SOP and polynomial forms Local transformations for EXOR expressions

Factorization of polynomials Validity check for EXOR networks

Fixed and mixed polarity polynomial forms Computing the coefficients of polynomial forms

Decision diagrams Techniques for functional decision tree construction

Functional decision tree reduction Further study Optimization of Computational

Structures Introduction Minterm and maxterm expansions Optimization of Boolean functions in algebraic form

Implementing SOP expressions using logic gates Minimization of Boolean functions using

K-maps Boolean function minimization using decision diagrams

Optimization of Boolean functions using decision trees

Decision diagrams for symmetric Boolean functions

Measurement of the efficiency of decision diagrams

Representation of multi-output Boolean functions Embedding decision diagrams into lattice structures

Further study Multivalued Data Structures

Introduction Representation of multivalued functions

Multivalued logic Galois fields GF(m)

Fault models based on the concept o

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