Prove that |R[0,1)| <= |F| where F is the set of all functions from N to {0,1}

Question

I believe that I need to show that there's a one-to-one function from R[0,1) to F and that I can do this by associating the decimal expansion .b_1b_2b_3... etc with a function f(n) that is either 0 or 1 based on some property of the digit b_n in the decimal expansion. I'm having trouble coming up with such a function.