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