If a function assigns 0 or 1 to each switching function of \(n\) variables, how many such functions are there?

There are \(2^{2^n}\) switching functions of \(n\) variables. For each such function we have two choices (0 or 1) so we need to multiply 2 by itself \(2^{2^n}\) times resulting in:

\[2^{2^{2^n}}\]