Computer Arithmetics for Nanoelectronics

 Content: 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