# carry out of full adder

In a Full Adder what's wrong with [c.(a+b) + a.b] as the expression of the Carry-Out? I checked it with truth table and gives correct output. But in all books the expression is [c.(a XOR b) + a.b].

• Both are correct – sarthak Oct 12 '17 at 9:44

You can write $(A + B)$ as $A\cdot B + A \oplus B$.
$C \cdot(A+B) + A\cdot B = C \cdot (A\oplus B) + C \cdot A \cdot B + A\cdot B =\\ = C \cdot (A\oplus B) + (1+C) \cdot A \cdot B = C \cdot (A\oplus B) + A \cdot B$
The books use the latter formula because you don't need to calculate again $A \oplus B$, because you can reuse the sum term $S=A\oplus B$ (i.e. you save one logic gate).