When two 8-bit numbers $A_{7}\cdots A_{0}$ and $B_{7}\cdots B_{0}$ in 2's…

GATE · 2017 · CS · Set 1 · Computer Science & IT

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

A.
the carry bit $C_{7}$ is 1
B.
all the carry bits $\left ( C_{7},\cdots ,C_{0} \right )$ are 1
C.
$\left ( A_{7} \cdot B_{7} \cdot \overline{S_{7}}+\overline{A_{7}} \cdot \overline{B_{7}} \cdot S_{7} \right )$ is 1
D.
$\left ( A_{0} \cdot B_{0} \cdot \overline{S_{0}}+\overline{A_{0}} \cdot \overline{B_{0}} \cdot S_{0} \right )$ is 1

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When two 8-bit numbers \(A_{7}\cdots A_{0}\) and \(B_{7}\cdots B_{0}\) in 2's…