Research On Tabular Method Of Digital Theory

As digital eireuit grows larger and the design task becomes more complex,traditional digital theory can't meet the requirement, and must be studied further.Modern digital theory is the answer which researehs the traditional digital theoryfurther. It not only extends the contents of digital theory greatly, but also proposesmany new methods. Combined with the production of modern digital theory, tabularmethods of digital theory are systematically discussed in this dissertation.Some special logic operations and special logic functions are introduced inmodern digital theory, and they are important contents that modern digital theoryresearch. The definitions and characteristics of these special logic operations andspecial logic functions are analyzed in this paper. Based upon this, the characteristicsof Boolean difference and Boolean partial derivative are studied farther, and therelationships between them and spectral coefficients are proposed. After dicussed therelationships between Boolean difference and Boolean partial derivative and speciallogic functions in detail, the paper proposes several theorems, and proves them. Theserelationships and characteristics can make the detection and judgment for speciallogic functions more convenience.And-Or-Not algebraic system is a traditional Boolean algebraic system. Thisdissertation introduces all kinds of tabular methods for function expression in thisalgebraic system, and discusses all forms and characteristics of tabular in detail, at thesame time; the compression method of truth value table is presented. All existingtabular methods are dicussed systematically in this thesis, and the methods ofcalculating first-order and n-order Boolean difference by using decomposition tabularare presented. By using these methods, the tabular methods of detecting special logicfunctions are proposed, and some examples prove the methods. Considering thepartially described logic function, we propose the conception of correlative arbitraryitem and the tabular with arbitrary item. By using this tabular, a series of tabularmethods of calculating special operations and detecting special logic functions arepresented in this thesis, and some examples are given to explain. These methods willcomplement and consummate the tabular methods of And-Or-Not algebraic system.Modular algebraic system has several advantages such as easy to detection,convenient for synthesis, so it becomes a hotspot in digital theory research. The paperdicusses expression forms and characteristics of product item tabular, and introducesexiting tabular methods systematically. Based upon these, the tabular methods ofdetecting symmetry (including partial negated variables) and calculating Booleandifference and Boolean partial derivative of RM type function are proposed. Thearbitrary item in modular algebraic system is more complicated than in And-Or-Notalgebraic system. By analyzed and compared carefully, the expression form of tabular with arbitrary item is dieussed, and a series of tabular methods are presented in thisthesis by using the tabular with arbitrary item.OR-coincidence algebraic system has close relationship with modular algebraicsystem, so it is necessary to study this algebraic system. Considering the properties ofcoincidence operation, the paper discusses sum term tabular in detail, proposesseveral practical characteristics, and verifies them. We also analyze the properties ofBoolean difference and partial derivative and some special logic functions inOR-coincidence algebraic system in this thesis, and give some tabular methods tocalculating Boolean partial derivative and difference of OC type logic functions.