  We construct the exact noncommutative solutions on tori. This gives an exact
description of tachyon condensation on bosonic D-branes, non-BPS D-branes and
brane-antibrane systems. We obtain various bound states of D-branes after the
tachyon condensation. Our results show that these solutions can be generated by
applying the gauge Morita equivalence between the constant curvature projective
modules. We argue that there is a general framework of the noncommutative
geometry based on the notion of Morita equivalence which underlies this
specific example.
