  We present a high statistics lattice calculation of the B--meson binding
energy $\overline{\Lambda}$ of the heavy--quark inside the pseudoscalar
B--meson. Our numerical results have been obtained from several independent
numerical simulations at $\beta=6.0$, $6.2$ and $6.4$, and using, for the meson
correlators, the results obtained by the APE group at the same values of
$\beta$. Our best estimate, obtained by combining results at different values
of $\beta$, is $\overline{\Lambda}=180^{+30}_{-20}$ MeV. For the
$\overline{MS}$ running mass, we obtain
$\overline{m}_{b}(\overline{m}_{b})=4.15 \pm 0.05 \pm 0.20$ GeV, in reasonable
agreement with previous determinations. The systematic error is the truncation
of the perturbative series in the matching condition of the relevant operator
of the Heavy Quark Effective Theory.
