2.4 Boolean Logic

• AND Both inputs need to be **TRUE** in order for the output to be **TRUE**. • OR Only one of the inputs need to be true in order for the output to be true • NOT This reverses the Input

Why data is represented in binary form A computer is basically a collection of transistors and circuits. These components have two states: • on - a current is flowing through the component • off - a current is not flowing through the component These two states can easily be represented by using binary: • 1 = on (TRUE) • 0 = off (FALSE) State State refers to the output of a circuit. If a circuit has one input and one output, and the input and output each have two states - on and off - this gives two combinations of state: • input off, output off • input on, output on More complex circuits have many inputs, and the output state depends on the various combinations of the inputs and the logic gates they pass into. Logic gates In its most basic form, a computer is a collection of powered and unpowered circuits and transistors. A logic gate is a series of transistors connected together to give one or more outputs, each output being based on the input or combination of inputs supplied to it. There are three types of gate to consider: • AND gate • OR gate • NOT gate Each type of gate can be represented either as a diagram, in algebraic form, or as a truth table. Boolean algebra Boolean algebra is a notation used to represent logic. For example: • Q = A AND B • Q = A OR B • Q = NOT A This notation can also be represented using symbols: • Q = A /\ B, or as A.B • Q = A \/ B, or as A+B • Q = ¬ A