Why do Boolean functions play a central role in hardware architectures?

Boolean algebra deals with the Boolean (also called binary) values that are typically labeled true/false, 1/0, yes/no, on/off, and so forth. A Boolean function is a function that operates on binary inputs and returns binary outputs. Since computer hardware is based on the representation and manipulation of binary values, Boolean functions play a central role in the specification, construction, and optimization of hardware architectures.