Tabular Method And Its Application In OR-Coincidence Algebra System

The development of the methodology in Modern Digital Theory is firmly related to the Modern Digital Theory. From traditional Boolean Digital algebra system's truth table method, Karnaugh map to AND-XOR b_j map, and OR-Coincidence d_j map, they gave huge improvement to the development of the methodology of Modern Digital Theory. And tabular method as the way of research of Modern Digital Theory has been used for a long time, too.The dissertation is focused on the Tabular Method and its application in the OR-Coincidence algebra system.First of all, the concept of sum-term table was proposed. The feature of sum-term table, the transform of truth table and sum-term table was discussed. Furthermore, we proposed reduced-dimension sum-term table and sum-term table with mutually exclusive variables. Also, we presented the reduced-dimension method.Secondary, on the basis of GFOC, we proposed the method how to transfer the sum-term table between different polarities when it's the fixed-polarity. From the result of different polarities, it can be confirmed which is the simplest expansion of all. When it comes to the sum-term table with mutually exclusive variables, we also presented the method to simplify its expansion.In the last segment, the application of sum-term table was proposed. Based on reduced-dimension sum-term table, a new universal logic gate (ULG3) was found. And the other applications covered at the detection of redundant function, self-negative (SN) function and self-dual (SD) function using the sum-term table.It's clearly that tabular method which is the method used in the Modern Digital Theory will have a bright future, for its simplicity and programmability.