Full adder

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 CIN as inputs and S, COUT as outputs.

Truth table for full adder

A B CIN S COUT
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

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