GATE CS 2024 Set 1 — Question 13

In a 5-bit 2's complement system, the range of representable integers is from $-2^{5-1}$ to $2^{5-1}-1$, i.e., from $-16$ to $+15$.Given:
$A = 01010_2$. Since the MSB is 0, it is positive. Value $= +10$.
$B = 11010_2$. Since the MSB is 1, it is negative. To find the magnitude, we take the 2's complement: invert bits ($00101$) and add 1 ($00110$), which is 6. So, $B = -6$.Let's evaluate the options:(A) $A + B = 10 + (-6) = 4$. This is within the range $[-16, 15]$. No overflow.(B) $A - B = 10 - (-6) = 16$. The maximum positive value representable is 15. Since $16 > 15$, an arithmetic overflow occurs.(C) $B - A = -6 - 10 = -16$. This is within the range $[-16, 15]$. No overflow ($-16$ is represented as $10000_2$).(D) $2 * B = 2 * (-6) = -12$. This is within the range $[-16, 15]$. No overflow.Thus, the operation $A - B$ results in an overflow.