Show that there exists a bijection between $\mathbb{N^N}$ and $2^\mathbb N$.

Question

I have see somewhere that ${\aleph_0}^{\aleph_0}=2^{\aleph_0}$.That means that $|\mathbb{N^N}|=|2^\mathbb N|$.I want to show explicitly that there exists a bijection between $\mathbb {N^N}$ and $2^\mathbb N$ where $\mathbb N^\mathbb N$ denotes the set of all functions from $\mathbb N$ to $\mathbb N$ and $2^\mathbb N$ denotes the power set of $\mathbb N$.I do not know how to start with.Any hint will be helpful.