  The Hirota-Miwa equation can be written in `nonlinear' form in two ways: the
discrete KP equation and, by using a compatible continuous variable, the
discrete potential KP equation. For both systems, we consider the Darboux and
binary Darboux transformations, expressed in terms of the continuous variable,
and obtain exact solutions in Wronskian and Grammian form. We discuss
reductions of both systems to the discrete KdV and discrete potential KdV
equations, respectively, and exploit this connection to find the Darboux and
binary Darboux transformations and exact solutions of these equations.
