In this paper, we study inverse semigroups defined on the Bratteli-Vershik systems and SFT covers of  1 -solenoids.
We show that groupoids of germs of these inverse semigroups are equivalent to the unstable equivalence groupoids of  1 -solenoids.
And we prove that Exel's tight C*-algebras  of inverse semigroups are strongly Morita equivalent to the unstable  C*-algebras of 1 -solenoids.