Post Correspondence Problem for alphabets of size two The alphabet consists of just two characters, $0$ and $1$. How do I go about proving that it's undecidable? 
I was thinking of reducing the general case to binary form meaning if the alphabet has more than two characters encode them into binary. I don't really know how to go about proving it though.
Any help would be appreciated. Thanks

The question seems ambiguous, as there are two alphabets involved in the PCP. That is, we are given two morphisms $g, h: \Sigma^*\rightarrow\Delta^*$, and it is unclear which alphabet, $\Sigma$ or $\Delta$, is meant to be of size two. This is important as the solution depends on which alphabet has size two.
As every finitely generated free monoid embeds into $\{0, 1\}^*$, the problem is trivially undecidable for maps $g, h: \Sigma^*\rightarrow \{0, 1\}^*$. That is, suppose that the PCP is undecidable for maps $g', h': \Sigma^*\rightarrow\Delta^*$, with fixed alphabets $\Sigma$ and $\Delta$, and let $k: \Delta^*\rightarrow\{0, 1\}^*$ be an injective morphism. Then the PCP is undecidable for maps $kg', kh': \Sigma^*\rightarrow\{0, 1\}^*$.
On the other hand, the problem is actually decidable for maps of the form $g, h: \{0, 1\}^*\rightarrow\Delta^*$, as proven in A. Ehrenfeucht, J. Karhumäki, and G. Rozenberg, "The (generalized) Post correspondence problem with lists consisting of two words is decidable." Theoretical Computer Science 21.2 (1982): 119-144 (doi).
