  Exact results for the BPS index are known for a class of BPS dyons in type II
string theory compactified on a six dimensional torus. In this paper we set up
the problem of counting the same BPS states in a duality frame in which the
states carry only Ramond-Ramond charges. We explicitly count the number of
states carrying the lowest possible charges and find agreement with the result
obtained in other duality frames. Furthermore, we find that after factoring out
the supermultiplet structure, each of these states carry zero angular momentum.
This is in agreement with the prediction obtained from a representation of
these states as supersymmetric black holes.
