Let $\mathbb{B} = \{ 0, 1 \}$ be the D217: Set of boolean numbers.
Let $N \in \{ 1, 2, 3, \ldots \}$ be a D5094: Positive integer.
Let $N \in \{ 1, 2, 3, \ldots \}$ be a D5094: Positive integer.
Then
\begin{equation}
\# \left\{ f \mid f : \mathbb{B}^N \to \mathbb{B} \right\}
= 2^{2^N}
\end{equation}