I am trying to read about K-theory and differential K-theory. I understand that the K-theory of spheres can be computed explicitly (by getting to the stable range and using Bott periodicity and so on). Are there simple examples (of computation) for differential K-theory? Also, Gillet and Soule defined a holomorphic variant of the same (using Bott chern classes instead of Cheeger-Simons). Are there simple examples in their case where the K group maybe explicitly computed?