We have developed a new technique for use in two-dimensional Monte Carlo simulations which has been applied to hard-disc systems. The Voronoi tesselation of the system of particles is incorporated into the Monte Carlo simulations and provides easy access to nearest and next-nearest neighbours. The tesselation is dynamically maintained during the simulations and the computing time used is linear in N, the number of particles in the system. In addition, Voronoi statistics provide a method for examining the liquid/solid structure of the systems. Studies have been made on binary mixtures of hard-core discs in which the concentrations of the species are allowed to vary according to pre-set degeneracies. The concentrations would be expected to vary according to the pressure and packing fraction of the system. Scaled particle theory has been used to predict the behaviour of the systems in both the liquid and solid phases with a high degree of success.