Computer Arithmetics for Nanoelectronics

Emphasizes the Basic Principles of Computational Arithmetic and Computational Structure DesignTaking an interdisciplinary approach to the nanoscale generation of computer devices and systems, Computer Arithmetics for Nanoelectronics develops a consensus between computational properties provided by data structures and phenomenological properties of nano and molecular technology.
Covers All Stages of the Design Cycle, from Task Formulation to Molecular-Based ImplementationThe book introduces the theoretical base and properties of various data structures, along with techniques for their manipulation, optimization, and implementation. It also assigns the computational properties of logic design data structures to 3D structures, furnishes information-theoretical measures and design aspects, and discusses the testability problem. The last chapter presents a nanoscale prospect for natural computing based on assorted computing paradigms from nature.
Balanced Coverage of State-of-the-Art Concepts, Techniques, and PracticesUp-to-date, comprehensive, and pragmatic in its approach, this text provides a unified overview of the relationship between the fundamentals of digital system design, computer architectures, and micro- and nanoelectronics.

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 of change
Polynomial representations of multivalued logic functions
Polynomial representations using arithmetic operations
Fundamental expansions
Further study
Computational Networks
Introduction
Data transfer logic
Implementation of Boolean functions using multiplexers
Demultiplexers
Decoders
Implementation of switching functions using decoders
Encoders
Design examples
Design example: magnitude comparator
Design example: BCD adder
The verification problem
Decomposition
Further study
Sequential Logic Networks
Introduction
Physical phenomena and data storage
Basic principles
Data structures for sequential logic networks
Latches
Flip-flops
Registers
Counters
Sequential logic network design
Mealy and Moore models of sequential networks
Data structures for analysis of sequential networks
Analysis of sequential networks with various types of flip-flops
Techniques for the synthesis of sequential networks
Redesign
Further study
Memory Devices for Binary Data
Introduction
Programmable devices
Random-access memory
Read-only memory
Memory expansion
Programmable logic
Field programmable gate arrays
Further study
Spatial Computing Structures
Introduction
The fundamental principles of 3D computing
Spatial structures
Hypercube data structure
Assembling of hypercubes
N-hypercube
Embedding a binary decision tree into an N-hypercube
Assembling N-hypercubes
Representation of N-hypercubes using H-tree
Spatial topological measurements
Further reading
Linear Cellular Arrays
Introduction
Linear arrays based on systolic computing paradigm
Spatial systolic arrays
Linear arrays based on linear decision diagrams
Linear models of elementary functions
Logic networks and linear decision diagrams
Linear models for logic networks
Linear models for multivalued logic networks
Linear word-level representation of multivalued functions using logic operations
3D computing arrays design
Further study
Information and Data Structures
Introduction
Information-theoretical measures
Information-theoretical measures
Information measures of elementary switching function of two variables
Information-theoretical measures in decision trees
Information-theoretical measures in multivalued functions
Ternary and pseudo-ternary decision trees
Further reading
Design for Testability
Introduction
Fault models
Controllability and observability
Functional decision diagrams for computing Boolean differences
Random testing
Design for testability techniques
Further study
Error Detection and Error Correction
Introduction
Channel models
The simplest error detecting network
Discrete memoryless channel
Linear block codes
Cyclic codes
Block codes
Arithmetic codes
Further study
Natural Computing
Introduction
Fundamentals of the intermediate data structures
Self-assembling
Fractal-based models for self-assembly
Logic network design using directed evolution
Neural-based computing
Further study
Index