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Previous Year Question (PYQs)

Let $R_1$ and $R_2$ be two $4$-bit registers that store numbers in $2$'s complement form. For the operation $R_1+R_2$, which one of the following values of $R_1$ and $R_2$ gives an arithmetic overflow?




Solution

In $4$-bit $2$'s complement, range is

$-8$ to $+7$

Check option (b):

$R_1=1100=-4$

$R_2=1010=-6$

So,

$R_1+R_2=-4+(-6)=-10$

But $-10$ is outside the range $-8$ to $+7$.

Therefore, arithmetic overflow occurs.

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