  The $N=2 \;a=-2$ supersymmetric KdV equation is studied. A Darboux
transformation and the corresponding B\"acklund transformation are constructed
for this equation. Also, a nonlinear superposition formula is worked out for
the associated B\"acklund transformation. The B\"{a}cklund transformation and
the related nonlinear superposition formula are used to construct integrable
super semi-discrete and full discrete systems. The continuum limits of these
discrete systems are also considered.
