Consider a system that uses 5 bits for representing signed integers in 2’s complement format. In this system, two integers $A$ and $B$ are represented as $A=01010$ and $B=11010$. Which one of the following operations will result in either an arithmetic overflow or an arithmetic underflow?

In a 5-bit 2's complement representation, the range of representable signed integers is:

First, convert the binary representations of $A$ and $B$ to decimal:

• $A = 01010_2 = +(8 + 2) = +10$

• $B = 11010_2 = -16 + 8 + 2 = -6$

Now evaluate each option:

• (A) $A + B$: $10 + (-6) = +4$. Since $+4 \in [-16, +15]$, no overflow/underflow occurs.

• (B) $A - B$: $10 - (-6) = +16$. Since $+16 > +15$, this results in an arithmetic overflow.

• (C) $B - A$: $-6 - 10 = -16$. Since $-16 \in [-16, +15]$, no overflow/underflow occurs.

• **(D) $2 * B$:** $2 \times (-6) = -12$. Since $-12 \in [-16, +15]$, no overflow/underflow occurs.

Therefore, operation (B) results in an arithmetic overflow.