Overflow condition in $2's$ complement number system:-
- $c_{3} = 1,c_{4} = 1\implies$ No overflow
- $c_{3} = 0,c_{4} = 0\implies$ No overflow
- $c_{3} = 1,c_{4} = 0\implies$ Overflow $(a_{3} = b_{3} = 0)$
- $c_{3} = 0,c_{4} = 1\implies$ Overflow $(a_{3} = b_{3} = 1)$
We can conclude that the overflow condition for $2's$ complement number system is: $$c_{3}\oplus c_{4} = 1\\ \text{(OR)} \\ \bar{a_{3}}\cdot \bar{b_{3}}\cdot s_{3} + a_{3}\cdot b_{3}\cdot\bar{s_{3}} = 1$$
Here, we used $4-bit$ binary full adder and Ex-OR gate.
The Ex-OR gate is used to check the overflow condition.