We study the binding of E. coli single-stranded binding protein (SS) to single-stranded DNA (ssDNA) using a solid-state nanopore assay. We find that saturated nucleoprotein complexes can be distinguished easily from free SSB, ssDNA, or double-stranded DNA individually and demonstrate that the high affinity of SSB for ssDNA can be exploited to achieve high-fidelity differentiation from duplex molecules in a mixture. We then study nucleoprotein filament formation by systematically varying the amount of SSB relative to ssDNA. We,observe a concomitant shift in the mean amplitude of electrical events that is consistent with weakly cooperative binding. Finally, we compare circular and linearized ssDNA saturated with SSB and use the results to infer structural details of the nucleoprotein complex.