Just create 4 digits groups in every possible number between 0 and 1.

In pos 1 and 3 there will be only 0 or 1(valid or invalid)

In pos 2 the "entire part" of any real number: while you need digits, you write, in pos 1 a "1", when you finish writting the "entire" part, in each group of 4 digits, you will write a "0"... no matter wich digit you write there, probably a 0 or 7...since it has a 0 in pos1 is an invalid digit.

Make the same to write de decimal part of the real number in pos 4 of each group of 4 digits, if you need finish, write zeros in pos 3, if it has infinite decimal, all positions 3 are 1.

If I am not wrong, in this way you can write every real number just using numbers between 0 and 1, and you will not use all of them.

For example: 123,00897
0,

1110

1210

1318

0719

0717

(and here you can use any codifications that fits)

0707

0707.. until infinite decimal

PI:

0,

1311

0714

0711

0716

...