Let us first see about 2's Complement Numbers
The range of n-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)
So, we can generalize that $2^{n}$ distinct integers are possible with n-bit 2's Complement Number =====> X
Sign & Magnitude
The range of n-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 these are not distinct
Now, we can generalinze $2^{n}-1$ distinct Integers are possibe with n-bit Sign & Magnitude number ======>Y
X-Y = $2^{n}$ - ($2^{n}-1$)
= 1