The freezing mechanism, recently suggested for a monodisperse hard-disk fluid [Huerta et al, Phys. Rev. E, 2006, Vol. 74, 061106] is extended here to an equimolar binary hard-disk mixtures. We are showing that for diameter ratios, smaller than 1.15 the global orientational order parameter of the binary mixture behaves like in the case of a monodisperse fluid. Namely, by increasing the disk number density there is a tendency to form a crystalline-like phase. However, for diameter ratios larger than 1.15 the binary mixtures behave like a disordered fluid. We use some of the structural and thermodynamic properties to compare and discuss the behavior as a function of diameter ratio and packing fraction.