NIMCET 1s Complement 2s Complement Previous Year Questions (PYQs) – Page 1 of 3

For $9$-bit $1$'s complement, the range is

$-(2^{8}-1)$ to $+(2^{8}-1)$

$=-255$ to $+255$

Also, in $1$'s complement, there are two representations of zero: positive zero and negative zero.

So, statement I is correct.

For $9$-bit $2$'s complement, the range is

$-2^8$ to $2^8-1$

$=-256$ to $+255$

But $1$'s complement does not represent exactly $512$ unique values because zero has two representations.

So, statement II is incorrect.

The maximum positive number in both systems is

$+255$

So, statement III is correct.

Therefore, statements I and III only are correct.

For an n-bit system:

• 1’s complement range: $-(2^{n-1}-1)$ to $+(2^{n-1}-1)$ ⇒ smallest $=-(2^{8}-1)={-255}$.
• 2’s complement range: $-2^{n-1}$ to $+(2^{n-1}-1)$ ⇒ smallest $=-2^{8}={-256}$.

(9-bit means sign + 8 magnitude bits.)