Q7 (20 pts). N-bit adder for signed numbers in the 2's complement.
1-a) Please prove that the carry-in signal, $c_{n-1}$, at bit position $n-1$ of a ripple-carry adder can be expressed as $c_{n-1} = x_{n-1} \oplus y_{n-1} \oplus s_{n-1}$, where $x_{n-1}$ and $y_{n-1}$ are the two inputs and $s_{n-1}$ is the sum bit.
Hint: $s_{n-1} = x_{n-1} \oplus y_{n-1} \oplus c_{n-1}$
1-b) Please prove that the overflow flag logic, $f_o = c_n \oplus c_{n-1}$, can be written as $f_o = c_n \oplus x_{n-1} \oplus y_{n-1} \oplus s_{n-1}$
