Division algebra over 2-adic fields

Question

Let $D$ be the quaternion division algebra and $O$ be a maximal $\mathbb{Z}$-order in $D$, say the Hurwitz quaternion integers. It can be proved that $D$ and $O$ split at odd primes, that is $$D\otimes_\mathbb{Q}\mathbb{Q}_p=Mat_2(\mathbb{Q}_p)\text{ and }O\otimes_\mathbb{Z}\mathbb{Z}_p=Mat_2(\mathbb{Z}_p),$$ for all odd primes $p$. What are the structures of $D\otimes_\mathbb{Q}\mathbb{Q}_2$ and $O\otimes_\mathbb{Z}\mathbb{Z}_2$?