Let $N \in \{ 1, 2, 3, \ldots \}$ be a D5094: Positive integer such that

(i)	$X_0, X_1, \, \ldots, \, X_{N - 1} \in \text{Bernoulli}(1/2)$ are each a D3999: Standard Bernoulli random boolean number
(ii)	$X_0, X_1, \, \ldots, \, X_{N - 1}$ is an D2713: Independent random collection

A D5075: Random integer $Z \in \text{Random}(\mathbb{Z})$ is a uniformly random $N$-bit integer if and only if \begin{equation} Z \overset{d}{=} - X_{N - 1} 2^{N - 1} + \sum_{n = 0}^{N - 2} X_n 2^n \end{equation}