Название: Arithmetic and Algebraic Circuits
Автор: Antonio Lloris Ruiz, Encarnacion Castillo Morales
Издательство: Springer
Год: 2021
Страниц: 686
Язык: английский
Формат: pdf (true)
Размер: 19.2 MB

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.

Arithmetic Circuits are those digital circuits with inputs interpreted as numbers and whose outputs provide the results of some arithmetic operation over the inputs (addition, subtraction, multiplication, or division). These initial objectives (the elemental arithmetic operations) have been expanded so any mathematical function (trigonometrics, exponentials, logarithmics, etc.) is included as the purpose of the arithmetic circuits.

As a first definition, Algebraic Circuits are those digital circuits whose behaviour can be associated with any algebraic structure. Specifically, a polynomial is associated to each circuit, so that the evolution of the circuit will correspond to the algebraic properties of the polynomial. LFSRs (Linear Feedback Shift Registers) and CAs (Cellular Automata), included in this first denomination of algebraic circuits, are grouped under the name of basic algebraic circuits.

As a second definition, Algebraic Circuits are those digital circuits implementing the different operations within some algebraic structure. Specifically, in this book, this definition references to finite or Galois fields. The implementation of this algebraic circuits requires LFSRs and some basic arithmetic circuits.