2's Complement Representation
The range of $n\text{-bit}\; 2$'s Complement Numbers is $-(2^{n-1})$ to $+(2^{n-1}-1)$
For example, if $n = 2$, then $-2, -1, 0, 1$ belong to the range(which are distinct)
In general $2^{n}$ distinct integers are possible with $n\text{-bit}\;2's$ Complement Number $\to X$
Sign Magnitude Representation
The range of $n\text{-bit}$ Sign Magnitude numbers is $- (2^{n-1}-1)$ to $+ (2^{n-1}-1)$
For example, if $n = 2$, then $-1, -0, +0, +1$ belong to the range in which $-0 = +0$ and both represent zero.
In general $2^{n}-1$ distinct integers are possible with $n\text{-bit}$ Sign magnitude representation $\to Y$
$X-Y =2^{n} - (2^{n}-1) =1.$