just index on the number of ones. Ex 0.10110 there are two ones in a row, so reference those two ones to be the number two. For 00, flip it and refer to the same pair of ones.
That is totally missing the point. Of course for every number there is an encoding that contains all pieces of information.
That obviously applies to 0.00... = 0 as well, it contains 0, then 00, then 000 and so on. So every number and therefore every piece of information is contained in 0 as well, given the right encoding. Obviously if you can choose the encoding after choosing the number all number "contain" all information. That is very uninteresting though and totally misses the point.
