  A finite $p$-group $G$ is called \textit{powerful} if either $p$ is odd and
$[G,G]\subseteq G^p$ or $p=2$ and $[G,G]\subseteq G^4$. A {\em{cover}} for a
group is a collection of subgroups whose union is equal to the entire group. We
will discuss covers of $p$-groups by powerful $p$-subgroups. The size of the
smallest cover of a $p$-group by powerful $p$-subgroups is called the
\textit{powerful covering number}. In this paper we determine the powerful
covering number of the dihedral 2-groups.
