calculate the VC-dimension

I have a question about VC-dimension. I have this claim and I need to find out what its VC-dimension is

$ H\subseteq\{0,1\}^n $ collection of Boolean functions over n

In my opinion the answer should be that the rank of VC-dimension should be 3 or n + 1 but I'm not sure. By the definition of VC-dimension, the max rank will be equal to the size of the field +1. that means n+1.

I'm not sure why because the functions are binary, it can give a different answer. If the functions were at base 3, I would get a different answer, and not n + 1?