looking up data by splitting according to 'binary' value

[Zestje]

ORIGINAL QUESTION:
Hello,

I have a table like the following:
Example:

INDEX DATA
1.....A
2.....B
4.....C
8.....D
16.....E
32.....F
64.....G
128.....H

The counting is just like binary. I want to fill a cell with data by looking up a value from a cell, 'splitting' it according to the table and filling another cell by adding the looked up values as text.
So the value 3 corresponds to 'A B' (1 + 2). The value 57 corresponds with 'A D E F' (1 + 8 + 16 + 32).
I have not been able to find how to do this since I have no clue what this kind of function is called in excel and haven't been able to find the using a search.
Many thanks in advance for any help!

Moderator's note: Original Discussion

example file

Many thanks in advance for any help!