We report the structural behavior for mixtures of two differently sized (bidisperse) silica microspheres at the air-water interface under three different size ratio conditions (alpha (= R-S/R-L) = 0.375, 0.500, and 0.579). These bidisperse silica monolayers were studied via measurement of the surface pressure-area isotherm and optical microscopy at various particle surface coverages (theta = theta(S) + theta(L)) during compression. The silica colloids used in these trials were found to possess purely repulsive pair interactions at the air-water interface, which was confirmed by the pair correlation function calculated from the analysis of many optical images of the particles taken at dilute concentrations. The results revealed that, at certain mixture compositions (beta = theta(L)/theta(S)), compression can lead to the formation of 2D binary crystal structures. Specifically, at a particle size ratio of alpha = 0.375, LS1 crystal domains were observed at a surface coverage of theta approximate to 0.619 when beta = 7.00 and 3.50, although this LS1 structure was not observed at higher total particle densities (where the system became phase-separated). At a size ratio of alpha = 0.579, compression produced 2D LS2 binary crystals at particle surface coverages (theta) above 0.641 when beta = 3.00, 1.50, or 1.00. However, at a size ratio of alpha = 0.500, compression triggered macroscopic phase separation, leading to the formation of two separate hexagonal-close-packed domains consisting purely of either large or small particles. In general, when the mixture composition (beta) was too different from the stoichiometric ratio needed for the formation of LS1 or LS2 superlattices, the bidisperse monolayer was observed to remain in an amorphous state rather than evolving to an ordered phase under compression. These findings suggest that, in two dimensions, contrary to what has been speculated in the literature, (1) purely repulsive pair potentials can give rise to LS1 and LS2 binary crystals under compression and also (2) perfectly spherical particles can form LS2 crystals. This discrepancy between our results and the predictions of previous simulations might indicate that the capillary interaction and/or the many-body effects play a significant role in determining the structure of bidisperse colloids at the air-water interface