  When a spacetime has boundaries, the entangling surface does not have to be
necessarily compact and it may have boundaries as well. Then there appear a
new, boundary, contribution to the entanglement entropy due to the intersection
of the entangling surface with the boundary of the spacetime. We study the
boundary contribution to the logarithmic term in the entanglement entropy in
dimensions $d=3$ and $d=4$ when the entangling surface is orthogonal to the
boundary. In particular, we compute a boundary term in the entropy of
${\mathcal{N}}=4$ super-gauge multiplet at weak coupling. This result is
compared with the holographic calculation of the entropy based on the
Ryu-Takayanagi proposal adapted appropriately to the present situation. We find
a complete agreement between these two calculations provided the boundary
conditions imposed on the gauge multiplet preserve $1/2$ of the supersymmetry
and the extension of the boundary into the AdS bulk is a minimal hypersurface.
