Let $X_1, X_2, X_3, \ldots \in \text{Bernoulli}(1/2)$ each be a D3999: Standard Bernoulli random boolean number such that

(i)	$X_1, X_2, X_3, \ldots$ is an D2713: Independent random collection

A D3161: Random real number $U \in \text{Random}[0, 1]$ is a standard unsigned uniform random real number if and only if \begin{equation} U \overset{d}{=} \lim_{N \to \infty} \sum_{n = 1}^N \frac{X_n}{2^n} \end{equation}