196

Full – Adder

This circuit needs three binary inputs and two binary outputs. The truth table for a full-adder is:

• Two of the input variable ‘x’ and ‘y’, represent the two significant bits to be added.
• The third input variable ‘z’, represents the carry from the previous lower significant position.
• The outputs are designated by the symbol ‘S’ for sum and ‘C’ for carry.
• The eight rows under the input variables designate all possible combinations of 0’s, and 1’s that these variables may have.
• The input-output logical relationship of the full-adder circuit may be expressed in two Boolean functions, one for each output variable.
• Each output Boolean function can be simplified by using a unique map method.

Maps for a full-adder:

The logic diagram for a full-adder circuit can be represented as: