DIGITAL LOGIC: GATES

•          The basic gates used in digital logic are AND,OR, NOT, NAND, NOR, and XOR.
•    The inversion (NOT) operation is indicated by a circle.
•    All of the gates except NOT can have more than two inputs.

•          to assert a signal is to cause signal line to make a transition from its logically false (0) state to its logically true (1) state.
•      it is important to identify functionally complete sets of gates.
•        any Boolean function can be implemented using only the gates in the set.
•        The following are functionally complete sets:

• AND, OR,NOT

• AND,NOT

• OR,NOT

• NAND

• NOR

• 
  
•      AND, OR, and NOT gates constitute a functionally complete set, because they represent the three operations of   Boolean algebra.
•      For the AND and NOT gates to form a functionally complete set, there must be a way to synthesize the OR   operation from the AND and NOT operations.
•        This can be done by applying DeMorgan’s theorem:

                                                                                 ____

                                                                                           A + B  = Ā . B̅

    A OR B = NOT ((NOT A) AND (NOT B))

NOR Gate Implementation

•         Similarly, the OR and NOT operations are functionally complete because they can be used to synthesize the  AND operation.