Looking for a generalised or non-iterative maths equation for the process of slicing up a range value

Question

Suppose I have a integer range $[0,n]$ and an integer $x$ within that range.

Suppose I can generate an integer $y$ though this iterative process:

1. $x$ is converted to Base 2
2. For each bit from most to least significant:
   • If 0 then cut the current number range in half, keeping the upper half as the new range.
   • If 1 then cut the current number range in half, keeping the lower half as the new range.
3. Once there are no more bits, $y$ is the current value of $n$.

Is there a maths equation that can solve for $y$ without this iteration?

Indeed, is there any generalised equation or known algorithm for this behaviour?

_{N.B. Feel free to change the question title if you know the type of equation or algorithm this is.}