用线性代数建模数字切换电路

English | PDF(True) | 2014 | 161 Pages | ISBN : 162705233X | 1.73 MB

Modeling Digital Switching Circuits with Linear Algebra describes an approach for modeling digital information and circuitry that is an alternative to Boolean algebra. While the Boolean algebraic model has been wildly successful and is responsible for many advances in modern information technology, the approach described in this book offers new insight and different ways of solving problems. Modeling the bit as a vector instead of a scalar value in the set {0, 1} allows digital circuits to be characterized with transfer functions in the form of a linear transformation matrix. The use of transfer functions is ubiquitous in many areas of engineering and their rich background in linear systems theory and signal processing is easily applied to digital switching circuits with this model. The common tasks of circuit simulation and justification are specific examples of the application of the linear algebraic model and are described in detail. The advantages offered by the new model as compared to traditional methods are emphasized throughout the book. Furthermore, the new approach is easily generalized to other types of information processing circuits such as those based upon multiple-valued or quantum logic; thus providing a unifying mathematical framework common to each of these areas.

Modeling Digital Switching Circuits with Linear Algebra provides a blend of theoretical concepts and practical issues involved in implementing the method for circuit design tasks. Data structures are described and are shown to not require any more resources for representing the underlying matrices and vectors than those currently used in modern electronic design automation (EDA) tools based on the Boolean model. Algorithms are described that perform simulation, justification, and other common EDA tasks in an efficient manner that are competitive with conventional design tools. The linear algebraic model can be used to implement common EDA tasks directly upon a structural netlist thus avoiding the intermediate step of transforming a circuit description into a representation of a set of switching functions as is commonly the case when conventional Boolean techniques are used. Implementation results are provided that empirically demonstrate the practicality of the linear algebraic model.

《用线性代数建模数字切换电路》描述了一种不同于布尔代数的建立数字信息和电路的方法。虽然布尔代数模型已取得巨大成功，并负责现代信息技术中的许多进步，但本书介绍的方法提供了新的见解并以不同的方式解决问题。将位表示为向量而不是标量值{0, 1}集合，可以使数字电路用线性变换矩阵的形式表示转换函数。利用转换函数在许多工程领域都是普遍存在的，并且这种模型易于应用于基于线性系统理论和信号处理的数字化切换电路。 电路模拟和验证等常见任务是线性代数模型应用的具体例子，其详细描述也在书中给出。本书强调了新模型与传统方法相比的优势。此外，新的方法很容易推广到其他类型的电路信息处理，例如基于多值逻辑或量子逻辑的电路；从而提供了一个这些领域共有的数学框架。 《用线性代数建模数字切换电路》结合了实现该方法以完成电路设计任务所需的理论概念和实际问题。数据结构被描述，并展示了它们在表示底层矩阵和向量方面所需资源与目前基于布尔模型的现代电子设计自动化（EDA）工具所使用的资源一样少。算法描述了执行有效模拟、验证和其他常见EDA任务的方法，这些方法竞争性地与传统设计工具。线性代数模型可以直接将EDA任务应用于结构网表，从而避免使用常规布尔技术时通常需要转换电路描述以表示一组切换函数的中间步骤。提供了实施结果来实证显示线性代数模型的实际可行性。

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