When two 8-bit numbers $A_7 \cdots A_0$ and $B_7 \cdots B_0$ in 2's complement representation (with $A_0$ and $B_0$ as the least significant bits) are added using a ripple-carry adder, the sum bits obtained are $S_7 \cdots S_0$ and the carry bits are $C_7 \cdots C_0$. An overflow is said to have occurred if

In 2's complement addition of two signed numbers $A$ and $B$, overflow occurs if and only if:

1. Adding two positive numbers results in a negative number: $A_7 = 0$, $B_7 = 0$, and $S_7 = 1$. The boolean condition for this case is $\overline{A_7} \cdot \overline{B_7} \cdot S_7 = 1$.

2. Adding two negative numbers results in a positive number: $A_7 = 1$, $B_7 = 1$, and $S_7 = 0$. The boolean condition for this case is $A_7 \cdot B_7 \cdot \overline{S_7} = 1$.

Combining both conditions, the overflow detection formula is:

Thus, an overflow occurs if $(A_7 \cdot B_7 \cdot \overline{S_7} + \overline{A_7} \cdot \overline{B_7} \cdot S_7) = 1$.

Hence, (C) is the correct option.