$2.$ Can you count the bit strings?

A bit string is a string of bits that have values of either $1$ or $0.$ A super bit string is a bit string made by flipping zero or more of the $0$s in the bit string to $1.$

Given k decimal integers, convert each to a bit string that has a given length n$.$ Generate all possible super bit strings of each of the k bit strings. Finally, perform a union of the super bit strings of all the bit strings and determine its size. This is the number to return.

For example, the required bit string length, n $=5,$ there are k $=2$

decimal integers, bitStrings $=[10,26]$ which when converted to

strings equal $[01010,11010].$ Note that the value $10$ had to be padded with a zero to make it the required length.