  Hatayama et al. conjectured fermionic formulas associated with tensor
products of U'_q(g)-crystals B^{r,s}. The crystals B^{r,s} correspond to the
Kirillov--Reshetikhin modules which are certain finite dimensional
U'_q(g)-modules. In this paper we present a combinatorial description of the
affine crystals B^{r,1} of type D_n^{(1)}. A statistic preserving bijection
between crystal paths for these crystals and rigged configurations is given,
thereby proving the fermionic formula in this case. This bijection reflects two
different methods to solve lattice models in statistical mechanics: the
corner-transfer-matrix method and the Bethe Ansatz.
