【作者】 肖林荣；

【导师】 陈偕雄；

【作者基本信息】 浙江大学 ， 电路与系统， 2005， 硕士

【摘要】 作为二值数字电子学的基础，传统的数字理论——布尔代数中基于与或非三种基本运算的代数系统的研究早已成熟。为了开拓新的数字元件及新一代数字电路，人们一直十分重视有关代数理论的研究，从而形成了近代数字理论。本文的主要内容是围绕着近代数字理论中的特殊运算展开的。 首先，通过与普通代数相对比，引入了近代数字理论中的各种特殊运算——布尔减、布尔除运算；布尔差分、布尔微分及布尔积分；以及模减、模除、模指数等运算。在此基础上，提出了基于布尔四则运算的代数系统，包括各种新的完备集、函数的规范展开式及化简、各种规范展开式之间的相互转换等。 其次，介绍了基于模四则运算的多值模代数系统：由模加、模减、模乘、模除等组成的各种模运算完备集的构成、函数展开、图形表示及其化简等。 此外，还讨论了特殊运算——布尔差分、布尔微分及布尔积分等的理论计算以及在故障检测中的应用。更多还原

【Abstract】 As a basis of the binary value digital electronic, the traditional digitaltheory --Boolean algebraic system which is based on and, or, notoperations--has already been developed. In order to develop new electronicdevices and electric circuit, it has been paid a lot of attention to study concerned algebraic theory and formed the modern digital theory. This dissertation is going to discuss the special operations in the modern digital theory.Firstly, this dissertation introduces the special operations in comparisonwith the basic algebra-- Boolean subtraction, Boolean division; Booleandifferential and integral calculus; modular subtraction, modular division, modular exponent and so on. On the base, it is proposed some of new algebraic systems on Boolean four arithmetic operations, which include some new complete sets, the logical function’s expansions and their minimization, the transform between the standard expansions etc.Then, multi-valued modular algebraic systems were surveyed on multi-valued modular four arithmetic operations in this dissertation, which include some new complete sets , the logical function’s expansions, their minimization and so on.In addition, this dissertation’ discusses Boolean differential, integral calculus and their application to detection of digital circuit faults .更多还原