Digital circuits are being used more and more in electronics, not only in computers but also in applications such as measurement, automatic control, robotics, and in situations requiring decisions. All of these applications require complex switching circuits that are formed from the five basic logic gates the AND, OR, NAND, and NOR gates and the inverter.
The significant point about these logic gates is that they only have two operating conditions. They are either ON (1) or OFF (0). When logic gates are interconnected to form more complex circuits, it is necessary to obtain the simplest circuit possible.
Boolean algebra offers a means of expressing complex switching functions in equation form. A Boolean expression is an equation that expresses
the output of a logic circuit in terms of its input. Veitch diagrams and Karnaugh maps provide a fast and easy way to reduce a logic equation to its simplest form.