  In the binary-alloy with composition A$_x$B$_{1-x}$ of two atoms with ionic
energy scales $\pm\Delta$, an apparent Ander- son insulator (AI) is obtained as
a result of randomness in the position of atoms. Using our recently developed
technique that combines the local self-energy from strong-coupling perturbation
theory with the transfer matrix method, we are able to address the problem of
adding a Hubbard $U$ to the binary alloy problem for millions of lattice sites
on the honeycomb lattice. By adding the Hubbard interaction $U$, the resulting
AI phase will become metallic which in our formulation can be clearly
attributed to the screening of disorder by Hubbard $U$. Upon further increase
in $U$, again the AI phase emerges which can be understood in terms of the
suppressed charge fluctuations due to residual Hubbard interaction of which the
randomness takes advantage and localizes the quasi-particles of the metallic
phase. The ultimate destiny of the system at very large $U$ is to become a Mott
insulator (MI). We construct the phase diagram of this model in the plane of
($U,\Delta$) for various compositions $x$.
