Theory of Expansion Boolean Algebra and Its Applications in CMOS VLSI Digital Systems

摘要

Based on the relationship between circuits (systems) and the signals in the circuits (systems), the theory of expansion Boolean algebra is presented in this paper. Static complementary logic circuits and static pass transistors logic circuits have been used to implement the high-speed and low-power-consumption cells circuits in CMOS VLSI systems. It is important to study the extraction method of logic expressions for these types of circuits. By analyzing the operations principles of MOS transistors in CMOS circuits, the theory of expansion Boolean algebra of CMOS logical circuits is presented. Based on the algebraic theory, a method of extracting the logic expressions from the two types of CMOS logical circuits is derived. On the basis of the method, a switch-level design method of CMOS logic circuits based on the algebra theory is presented, and the design method is used to design the high-speed and low-power full adder cells in CMOS VLSI systems. By the results of the simulation experiments, it is shown that the pass transistors and transmission gates hybrid CMOS full adder circuits proposed in this paper have a lower power-delay product by comparison with the full adder circuits designed by using other methods.