A continuous random quantity, $,$ is uniformly distributed over $(0,1).$ We wish to digitize

$($quantize$)$ as follows:

$1)$ First divide the interval $(0,1)$ into $2$ bins of with $=2.$

$2)$ Label each bin with a unique $-$bit binary word, $=[1,2,,].$ For example, we

might use a natural binary representation where the $$th bin could be represented by the

binary representation of the integer