Let $X$ be the number of distinct 16-bit integers in 2’s complement representation. Let $Y$ be the number of distinct 16-bit integers in sign magnitude representation. Then $X - Y$ is __________.

For an $n$-bit representation ($n = 16$):

1. 2's Complement Representation:

   • Range: $-2^{n-1}$ to $2^{n-1}-1$, which is $-32768$ to $+32767$.

   • Zero has a unique representation ($0000\,0000\,0000\,0000_2$).

   • Total distinct integers: $X = 2^{16} = 65536$.

2. Sign-Magnitude Representation:

   • Range: $-(2^{n-1}-1)$ to $+(2^{n-1}-1)$, which is $-32767$ to $+32767$.

   • Zero has two representations ($+0$ and $-0$).

   • Total distinct integers: $Y = 2^{16} - 1 = 65535$.

Therefore:

Thus, the value of $X - Y$ is 1.