Ive not clear how to pass from final interval to code value

I\'ve not clear how to pass from final interval to code value, for example:

Suppose we have the set of symbols={0,1,2,3} with probability={0.2, 0.5, 0.2 , 0.1} and that we have to encode a source S={2,1,0,0,1,3};

After the encoding process we\'ll have an interval [0.7426,0.7428).

Now the final step is to find the shortest representation to transmit and in the book the chosen value is 0.10111110001 = 0.74267578125.

How is it possible to calculate the shortest representation and the code value to transmit having the final interval?

Solution

One method that comes to mind is computing in tandem the next value (in lexicographic order), and storing enough bits to separate the two. This doesn\'t incur double computation, since most of the time carry lasts only for the few last symbols.