A logic gate is an electronic circuit that generates a typical output signal which depends on its input signal. Output signal of a gate is a general boolean operation of its input signal. Gates are fundamental logic elements which generate signals of binary 1 or 0.  We can signify any Boolean function in form of gates.

In general we can signify every gate by a distinct graphic symbol in addition its operation can be given through algebraic expression. To signify input-output relationship of binary variables in every gate truth tables are used. Notations and truth -tables for various logic gates are shown in Figure below.

Figure: Logic Gates

Truth table of NAND and NOR can be made from NOT (A AND B) and NOT (A OR B) correspondingly. Exclusive OR (XOR) is a special gate whose output is one only if two inputs aren't equal. Inverse of exclusive OR known as XNOR gate can be a comparator that will generate a 1 output if two inputs are equivalent.

Digital circuits use just one or two kinds of gates for simplicity in fabrication purposes. So one should think in terms of functionally complete set of gates. What does functionally complete set means? A set of gates by that any Boolean function can be realized is known as a functionally complete set. Functionally complete sets are: [AND, NOT], [NOR], [NAND], [OR, NOT].