Binary hard disc mixtures show eutectic freezing when the diameters differ by more than 30% and near the eutectic composition glasses can be formed without complications due to freezing. The glasses are characterized by measuring their equation of state and entropy. The glass transition is described by including the fluid and its many glasses within a unified formalism that represents the fluid as the collection of all its glasses. This leads to an equation of state that describes the fluid and the glasses from the ideal-gas, low-density limit to an ideal-glass high-density limit, with an ideal glass transition, where the heat capacity decreases sharply. The ideal transition is pre-empted by a kinetic glass transition that occurs when the root-mean-squared displacement of discs, on the simulation time scale, is comparable to a disc diameter.