Distribution of IEEE 754 single precision floating point over number line
The idea is that a (not denormalized) floating point number is stored as
$2^x \times 1.m_0 \ldots m_{k-1}$ (in binary),
where $x$ is the exponent and $m_0 \ldots m_{k-1}$ is the mantissa of length $k$. Two successive numbers with this exponent differ by $2^{x-k}$, since this minimal difference is $2^x \times 0.0\ldots01$, with $k-1$ zeroes after the dot. The minimal and maximal differences (among not denormalized numbers) are attained for the minimal and maximal $x$.