In a system, numbers are represented using 4-bit two's complement form. Consider four numbers $N1 = 1011$, $N2 = 1101$, $N3 = 1010$ and $N4 = 1001$ in the system. Which of the following operations will result in arithmetic overflow?

In a 4-bit two's complement representation, the range of representable numbers is:

Converting the given 4-bit two's complement binary numbers to decimal:

• $N1 = 1011_2 = -8 + 2 + 1 = -5$

• $N2 = 1101_2 = -8 + 4 + 1 = -3$

• $N3 = 1010_2 = -8 + 2 = -6$

• $N4 = 1001_2 = -8 + 1 = -7$

Now, evaluating each operation:

• (A) $N1 + N2 = (-5) + (-3) = -8$. Since $-8 \in [-8, 7]$, this does not cause overflow.

• (B) $N2 + N3 = (-3) + (-6) = -9$. Since $-9 < -8$, the result falls outside the representable range, resulting in arithmetic overflow.

• (C) $N3 - N4 = (-6) - (-7) = +1$. Since $+1 \in [-8, 7]$, this does not cause overflow.

• (D) $N1 + N4 = (-5) + (-7) = -12$. Since $-12 < -8$, the result falls outside the representable range, resulting in arithmetic overflow.

Thus, operations B and D result in arithmetic overflow.