Manipulating strings – How to use StringJoin in the following code?

Let alph = {"0", "1"}.
The following code returns {000, 001, 010, 011, 100, 101, 110, 111}

Flatten[
  Table[
    StringJoin[{alph[[a]], alph[[b]], alph[[c]]}],
{a, 1, length[alph]}, {b, 1, length[alph]}, {c, 1, length[alph]}]]

I'm trying to better understand the StringJoin order. How could I get a precursor {000, 001, 010, 011, 100, 101, 110, 111} using only the StringJoin command?