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Previous Year Question (PYQs)
Consider the following statements about the range of numbers in a $9$-bit $1$'s complement and $2$'s complement system.
I. In $9$-bit $1$'s complement, the range is $-255$ to $+255$, and there exist two representations of zero.
II. In $9$-bit $2$'s complement, the range is $-256$ to $+255$, and both $1$'s complement and $2$'s complement can represent exactly $512$ unique values.
III. The maximum positive number representable is $+255$ in both $1$'s complement and $2$'s complement $9$-bit systems.
Identify the CORRECT option.
Solution
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.
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