Let $n$ be a non-zero natural number and $\Phi_n : \{0,1\}^n \rightarrow \llbracket 0, 2^n - 1 \rrbracket$, $(x_j)_{j \in \llbracket 1,n \rrbracket} \mapsto \sum_{j=1}^{n} x_j 2^{n-j}$.
Specify $\operatorname{Im} \Phi_n$ as a function of $A_n$, where $A_n = \left\{\sum_{j=1}^{n} x_j 2^{n-j}, (x_j)_{j \in \llbracket 1,n \rrbracket} \in \{0,1\}^n\right\}$.