How to find the number of discrete states possible by current computers?
Acording to the suggestions that were given in the comments to the question, the number of distinct discrete states possible by a machine are related to the size the machine's of memory (or "stores" space, using Turing's nomenclature).

Since a bit has two distinct discrete states, a byte then have $$ 2^{2^3}=2^8 $$ discrete states. 

Two bytes, $$2^{2*2^3}=2^{16}$$

Hence, a commercial availabe 4GB DDR3 RAM machine would roughtly be $$ 2^{2^2*2^{30}*2^3} =2^{2^{35}}=2^{34,359,738,368} $$

Further, today's (March 2017) world fastest computer, Sunway TaihuLight, with more than 1 PB memory, would have rougthlty $$ 2^{2^{50}*2^3}=2^{53}=2^{9,007,199,254,740,992}$$ distinct discrete states.

Correct math if wrong, but the idea is this, taking in account only main memory (disregarding cpu registers, secondary memory and cache, as j_random_hacker stated that could be done).