  It has only recently been possible to study the superconducting state in the
attractive Hubbard Hamiltonian via a direct observation of the formation of a
gap in the density of states N(w). Here we determine the effect of random
chemical potentials on N(w) and show that at weak coupling, disorder closes the
gap concurrently with the destruction of superconductivity. At larger, but
still intermediate coupling, a pseudo-gap in N(w) remains even well beyond the
point at which off-diagonal long range order vanishes. This change in the
elementary excitations of the insulating phase corresponds to a crossover
between Fermi- and Bose-Insulators. These calculations represent the first
computation of the density of states in a finite dimensional disordered fermion
model via the Quantum Monte Carlo and maximum entropy methods.
