Boolean algebra , named after its pioneer George boole (1815-64), is the algebra of logic applied in the design and analysis of digital systems. The rules of this algebra are based on human reasoning. It originated from the study of how we reason, what lines of reasoning are valid and what constitutes proofs, etc. Boolean algebra is a mathematical system of logic in which truth functions are expressed as symbols and then these symbols are manipulated to arrive at conclusion.
Boolean functions can be performed by digital circuits. Circuits that perform complicated boolean functions can be subdivided into simpler circuits that perform simpler boolean functions. The circuits that perform the simplest boolean functions are taken as basic elements, called logic gates and are represented by specialized symbols. The logic gates are the OR, AND< NOT, NAND, NOR, Exclusive OR and Exclusive NOR gates. The NAND and NOR gates are called the universal gates. NOT gate or inverter is the only nontirvial single input gate.