Arithmetic Circuits
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Arithmetic Circuits
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Author : Amir Shpilka
language : en
Publisher: Now Publishers Inc
Release Date : 2010
Arithmetic Circuits written by Amir Shpilka and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.
A large class of problems in symbolic computation can be expressed as the task of computing some polynomials; and arithmetic circuits form the most standard model for studying the complexity of such computations. This algebraic model of computation attracted a large amount of research in the last five decades, partially due to its simplicity and elegance. Being a more structured model than Boolean circuits, one could hope that the fundamental problems of theoretical computer science, such as separating P from NP, will be easier to solve for arithmetic circuits. However, in spite of the appearing simplicity and the vast amount of mathematical tools available, no major breakthrough has been seen. In fact, all the fundamental questions are still open for this model as well. Nevertheless, there has been a lot of progress in the area and beautiful results have been found, some in the last few years. As examples we mention the connection between polynomial identity testing and lower bounds of Kabanets and Impagliazzo, the lower bounds of Raz for multilinear formulas, and two new approaches for proving lower bounds: Geometric Complexity Theory and Elusive Functions. The goal of this monograph is to survey the field of arithmetic circuit complexity, focusing mainly on what we find to be the most interesting and accessible research directions. We aim to cover the main results and techniques, with an emphasis on works from the last two decades. In particular, we discuss the recent lower bounds for multilinear circuits and formulas, the advances in the question of deterministically checking polynomial identities, and the results regarding reconstruction of arithmetic circuits. We do, however, also cover part of the classical works on arithmetic circuits. In order to keep this monograph at a reasonable length, we do not give full proofs of most theorems, but rather try to convey the main ideas behind each proof and demonstrate it, where possible, by proving some special cases.
Arithmetic And Algebraic Circuits
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Author : Antonio Lloris Ruiz
language : en
Publisher: Springer Nature
Release Date : 2021-03-27
Arithmetic And Algebraic Circuits written by Antonio Lloris Ruiz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-27 with Technology & Engineering categories.
This book presents a complete and accurate study of arithmetic and algebraic circuits. The first part offers a review of all important basic concepts: it describes simple circuits for the implementation of some basic arithmetic operations; it introduces theoretical basis for residue number systems; and describes some fundamental circuits for implementing the main modular operations that will be used in the text. Moreover, the book discusses floating-point representation of real numbers and the IEEE 754 standard. The second and core part of the book offers a deep study of arithmetic circuits and specific algorithms for their implementation. It covers the CORDIC algorithm, and optimized arithmetic circuits recently developed by the authors for adders and subtractors, as well as multipliers, dividers and special functions. It describes the implementation of basic algebraic circuits, such as LFSRs and cellular automata. Finally, it offers a complete study of Galois fields, showing some exemplary applications and discussing the advantages in comparison to other methods. This dense, self-contained text provides students, researchers and engineers, with extensive knowledge on and a deep understanding of arithmetic and algebraic circuits and their implementation.
Design Of Arithmetic Circuits In Quantum Dot Cellular Automata Nanotechnology
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Author : K. Sridharan
language : en
Publisher: Springer
Release Date : 2015-03-26
Design Of Arithmetic Circuits In Quantum Dot Cellular Automata Nanotechnology written by K. Sridharan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-26 with Technology & Engineering categories.
This research monograph focuses on the design of arithmetic circuits in Quantum Dot Cellular Automata (QCA). Using the fact that the 3-input majority gate is a primitive in QCA, the book sets out to discover hitherto unknown properties of majority logic in the context of arithmetic circuit designs. The pursuit for efficient adders in QCA takes two forms. One involves application of the new results in majority logic to existing adders. The second involves development of a custom adder for QCA technology. A QCA adder named as hybrid adder is proposed and it is shown that it outperforms existing multi-bit adders with respect to area and delay. The work is extended to the design of a low-complexity multiplier for signed numbers in QCA. Furthermore the book explores two aspects unique to QCA technology, namely thermal robustness and the role of interconnects. In addition, the book introduces the reader to QCA layout design and simulation using QCADesigner. Features & Benefits: This research-based book: ·Introduces the reader to Quantum Dot Cellular Automata, an emerging nanotechnology. ·Explores properties of majority logic. ·Demonstrates application of the properties to design efficient arithmetic circuits. ·Guides the reader towards layout design and simulation in QCADesigner.
High Performance Integer Arithmetic Circuit Design On Fpga
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Author : Ayan Palchaudhuri
language : en
Publisher: Springer
Release Date : 2015-07-06
High Performance Integer Arithmetic Circuit Design On Fpga written by Ayan Palchaudhuri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-06 with Technology & Engineering categories.
This book describes the optimized implementations of several arithmetic datapath, controlpath and pseudorandom sequence generator circuits for realization of high performance arithmetic circuits targeted towards a specific family of the high-end Field Programmable Gate Arrays (FPGAs). It explores regular, modular, cascadable and bit-sliced architectures of these circuits, by directly instantiating the target FPGA-specific primitives in the HDL. Every proposed architecture is justified with detailed mathematical analyses. Simultaneously, constrained placement of the circuit building blocks is performed, by placing the logically related hardware primitives in close proximity to one another by supplying relevant placement constraints in the Xilinx proprietary “User Constraints File”. The book covers the implementation of a GUI-based CAD tool named FlexiCore integrated with the Xilinx Integrated Software Environment (ISE) for design automation of platform-specific high-performance arithmetic circuits from user-level specifications. This tool has been used to implement the proposed circuits, as well as hardware implementations of integer arithmetic algorithms where several of the proposed circuits are used as building blocks. Implementation results demonstrate higher performance and superior operand-width scalability for the proposed circuits, with respect to implementations derived through other existing approaches. This book will prove useful to researchers, students and professionals engaged in the domain of FPGA circuit optimization and implementation.
Arithmetic Circuits For Dsp Applications
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Author : Pramod Kumar Meher
language : en
Publisher: John Wiley & Sons
Release Date : 2017-08-24
Arithmetic Circuits For Dsp Applications written by Pramod Kumar Meher and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-24 with Technology & Engineering categories.
A comprehensive guide to the fundamental concepts, designs, and implementation schemes, performance considerations, and applications of arithmetic circuits for DSP Arithmetic Circuits for DSP Applications is a complete resource on arithmetic circuits for digital signal processing (DSP). It covers the key concepts, designs and developments of different types of arithmetic circuits, which can be used for improving the efficiency of implementation of a multitude of DSP applications. Each chapter includes various applications of the respective class of arithmetic circuits along with information on the future scope of research. Written for students, engineers, and researchers in electrical and computer engineering, this comprehensive text offers a clear understanding of different types of arithmetic circuits used for digital signal processing applications. The text includes contributions from noted researchers on a wide range of topics, including a review of circuits used in implementing basic operations like additions and multiplications; distributed arithmetic as a technique for the multiplier-less implementation of inner products for DSP applications; discussions on look up table-based techniques and their key applications; CORDIC circuits for calculation of trigonometric, hyperbolic and logarithmic functions; real and complex multiplications, division, and square-root; solution of linear systems; eigenvalue estimation; singular value decomposition; QR factorization and many other functions through the use of simple shift-add operations; and much more. This book serves as a comprehensive resource, which describes the arithmetic circuits as fundamental building blocks for state-of-the-art DSP and reviews in - depth the scope of their applications.
Synthesis Of Arithmetic Circuits
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Author : Jean-Pierre Deschamps
language : en
Publisher: Wiley-Interscience
Release Date : 2006-03-10
Synthesis Of Arithmetic Circuits written by Jean-Pierre Deschamps and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-10 with Technology & Engineering categories.
A new approach to the study of arithmetic circuits In Synthesis of Arithmetic Circuits: FPGA, ASIC and Embedded Systems, the authors take a novel approach of presenting methods and examples for the synthesis of arithmetic circuits that better reflects the needs of today's computer system designers and engineers. Unlike other publications that limit discussion to arithmetic units for general-purpose computers, this text features a practical focus on embedded systems. Following an introductory chapter, the publication is divided into two parts. The first part, Mathematical Aspects and Algorithms, includes mathematical background, number representation, addition and subtraction, multiplication, division, other arithmetic operations, and operations in finite fields. The second part, Synthesis of Arithmetic Circuits, includes hardware platforms, general principles of synthesis, adders and subtractors, multipliers, dividers, and other arithmetic primitives. In addition, the publication distinguishes itself with: * A separate treatment of algorithms and circuits-a more useful presentation for both software and hardware implementations * Complete executable and synthesizable VHDL models available on the book's companion Web site, allowing readers to generate synthesizable descriptions * Proposed FPGA implementation examples, namely synthesizable low-level VHDL models for the Spartan II and Virtex families * Two chapters dedicated to finite field operations This publication is a must-have resource for students in computer science and embedded system designers, engineers, and researchers in the field of hardware and software computer system design and development. An Instructor Support FTP site is available from the Wiley editorial department.
Algebraic Circuits
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Author : Antonio Lloris Ruiz
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-04-05
Algebraic Circuits written by Antonio Lloris Ruiz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-05 with Technology & Engineering categories.
This book presents a complete and accurate study of algebraic circuits, digital circuits whose performance can be associated with any algebraic structure. The authors distinguish between basic algebraic circuits, such as Linear Feedback Shift Registers (LFSRs) and cellular automata and algebraic circuits, such as finite fields or Galois fields. The book includes a comprehensive review of representation systems, of arithmetic circuits implementing basic and more complex operations and of the residue number systems (RNS). It presents a study of basic algebraic circuits such as LFSRs and cellular automata as well as a study of circuits related to Galois fields, including two real cryptographic applications of Galois fields.
Low Complexity Arithmetic Circuit Design In Carbon Nanotube Field Effect Transistor Technology
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Author : K. Sridharan
language : en
Publisher: Springer Nature
Release Date : 2020-08-19
Low Complexity Arithmetic Circuit Design In Carbon Nanotube Field Effect Transistor Technology written by K. Sridharan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-19 with Technology & Engineering categories.
This book introduces readers to the emerging carbon nanotube field-effect transistor (CNTFET) technology, and examines the problem of designing efficient arithmetic circuits in CNTFET technology. Observing that CNTFETs make it possible to achieve two distinct threshold voltages merely by altering the diameter of the carbon nanotube used, the book begins by discussing the design of basic ternary logic elements. It then examines efficient CNTFET-based design of single and multiple ternary digit adders by judicious choice of unary operators in ternary logic, as well as the design of a ternary multiplier in CNTFET technology, and presents detailed simulation results in HSPICE. Lastly, the book outlines a procedure for automating the synthesis process and provides sample code in Python.
Formal Analysis Of Arithmetic Circuits Using Computer Algebra Verification Abstraction And Reverse Engineering
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Author : Cunxi Yu
language : en
Publisher:
Release Date : 2017
Formal Analysis Of Arithmetic Circuits Using Computer Algebra Verification Abstraction And Reverse Engineering written by Cunxi Yu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
Despite a considerable progress in verification and abstraction of random and control logic, advances in formal verification of arithmetic designs have been lagging. This can be attributed mostly to the difficulty in an efficient modeling of arithmetic circuits and datapaths without resorting to computationally expensive Boolean methods, such as Binary Decision Diagrams (BDDs) and Boolean Satisfiability (SAT), that require "bit blasting", i.e., flattening the design to a bit-level netlist. Approaches that rely on computer algebra and Satisfiability Modulo Theories (SMT) methods are either too abstract to handle the bit-level nature of arithmetic designs or require solving computationally expensive decision or satisfiability problems. The work proposed in this thesis aims at overcoming the limitations of analyzing arithmetic circuits, specifically at the post-synthesized phase. It addresses the verification, abstraction and reverse engineering problems of arithmetic circuits at an algebraic level, treating an arithmetic circuit and its specification as a properly constructed algebraic system. The proposed technique solves these problems by function extraction, i.e., by deriving arithmetic function computed by the circuit from its low-level circuit implementation using computer algebraic rewriting technique. The proposed techniques work on large integer arithmetic circuits and finite field arithmetic circuits, up to 512-bit wide containing millions of logic gates.
Digital Electronics 2
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Author : Tertulien Ndjountche
language : en
Publisher: John Wiley & Sons
Release Date : 2016-08-16
Digital Electronics 2 written by Tertulien Ndjountche and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-16 with Science categories.
As electronic devices become increasingly prevalent in everyday life, digital circuits are becoming even more complex and smaller in size. This book presents the basic principles of digital electronics in an accessible manner, allowing the reader to grasp the principles of combinational and sequential logic and the underlying techniques for the analysis and design of digital circuits. Providing a hands-on approach, this work introduces techniques and methods for establishing logic equations and designing and analyzing digital circuits. Each chapter is supplemented with practical examples and well-designed exercises with worked solutions. This second of three volumes focuses on sequential and arithmetic logic circuits. It covers various aspects related to the following topics: latch and flip-flop; binary counters; shift registers; arithmetic and logic circuits; digital integrated circuit technology; semiconductor memory; programmable logic circuits. Along with the two accompanying volumes, this book is an indispensable tool for students at a bachelors or masters level seeking to improve their understanding of digital electronics, and is detailed enough to serve as a reference for electronic, automation and computer engineers.