Spectral Logic and Its Applications for the Design of Digital Devices

CHAPTER 1

LOGIC FUNCTIONS

In the design of digital devices, many different ways are used to describe the input and output signals, and the input/output relations of the devices. The inputs and outputs are usually mathematically modeled by functions, while the input/output relations are represented by operators in some suitably selected function spaces. Combinational and sequential logic circuits alone can be viewed as particular examples of digital devices or as constitutes of their essential components.

In combinational logic circuits, the output is a (logic) function of inputs and, therefore, the input/output relations of these circuits are also represented by logic functions, or, conversely, combinational circuit realize (implement) logic functions.

In sequential circuits, the output depends also on the internal states of the circuit, and more sophisticated mathematical models, called sequential machines, are used for their representations. Combinational circuits are necessary parts of sequential circuits used to realize the output functions and state functions describing transitions between the states.

We will use several types of functions that vary with different sets as the domain and the range of the function to be able to represent the variety of the relations realized by digital devices. At the same time, representation of the same relations by functions with different domains and ranges may provide advantages in digital devices analysis, design, verification, testing, ...