For a number $x$, I would like to know whether there is a common name for the number $2^n$ such as $2^n \leq x < 2^{n+1}$ (e.g. If $x = 7$, then $2^n = 4$, $n = 2$).
I have some computer science related article where I extensively use such a number and I need a name to give it in order to explain how an algorithm works without having to repeat the number definition over and over every time I need to use it. I currently call it a "base $2$", saying for example that "$4$ is the base $2$ of $7$" (see example above), and that we need to "compute the base $2$ of the number", but this name feels wrong. Do you know whether a common name exists for such a number?
Note: actually, the article I am talking about deals with Gray codes. I am looking for a term that looks like it comes from math and not from computer science since many terms from computer science that deal with powers of two tend to be references to the usual binary representations of numbers. As an example, with Gray codes $2^3$ is 0b1100 and not 0b1000 so I am trying to avoid names that would literally mean the $n$th set bit, hence the question on Math.SE.
Note 2: as it has been highlighted in the many answers and comments, the goal of this question, once clearly reformulated, is to find a terse, pronounceable name for the function $2^{\lfloor \log_2(x) \rfloor}$ so that it is possible to say that "some number is the [insert name here] of $x$".
Best Answer
In the context of data structures - specifically, the van Emde Boas layout - I've heard this referred to as the hyperfloor of $x$. See “Cache-Oblivious B-Trees (Wayback Machine) by Bender, Demaine, and Farach-Colton for details - it defines the hyperfloor of $x$, denoted $\lfloor \lfloor x \rfloor \rfloor$, to be $2^{\lfloor \log_2 x \rfloor}$.
Hope this helps!