Research On Special Operations And Their Application In Modern Digital Theory

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 .