  Following the work of Sen, we consider the correspondence between extremal
black holes and string states in the context of the entropy. We obtain and
study properties of electrically charged black hole backgrounds of tree level
heterotic string theory compactified on a $p$ dimensional torus, for
$D=(10-p)=4 \ldots 9$. We study in particular a one--parameter extremal class
of these black holes, the members of which are shown to be supersymmetric. We
find that the entropy of such an extremal black hole, when calculated at the
stringy stretched horizon, scales in such a way that it can be identified with
the entropy of the elementary string state with the corresponding quantum
numbers.
