**Defined as :**

It is a logic circuit which performs the arithmetic sum of the three input bits i.e. addend bit,augend bit and a carry bit .

It has three input and two output. A, B and C_{IN} as inputs and S, C_{OUT} as outputs.

**Truth table for full adder
**

A |
B |
C_{IN} |
S |
C_{OUT} |

0 | 0 | 0 | 0 | 0 |

0 | 0 | 1 | 1 | 0 |

0 | 1 | 0 | 1 | 0 |

0 | 1 | 1 | 0 | 1 |

1 | 0 | 0 | 1 | 0 |

1 | 0 | 1 | 0 | 1 |

1 | 1 | 0 | 0 | 1 |

1 | 1 | 1 | 1 | 1 |

**Boolean expression** for Sum and Carry out can be derived using K – Map.

k map for SUM is below,

therefore,the simplified expression for sum is,

so, here we need four 3-input AND gate and one 4-input OR gate to design circuit for SUM.

Now ,the k-map for carry out is

and the simplified expression results for carry out is,

Similarly,we required three 2-input AND gate and one 3-input OR gate for carry circuit.

**LOGIC EXPRESSION for full adder**

**CIRCUIT DIAGRAM
**two level realization of FULL ADDER shown below,

we need two EXOR gates and 3 (two- input AND gate)with one (three -input OR gate) for designing full adder.Here the circuit diagram for full adder,

**LOGIC SYMBOL for full adder**

**FULL ADDER USING TWO HALF ADDERS logic diagram**