The electrical double layer near a charged electrode formed by a binary electrolyte in which the cations and anions have different diameters varying between 1.5 and 4.25 A is studied by Monte Carlo (MC) simulation. Our emphasis is on small electrode charge, where new phenomena may be expected. As one would expect, there is a nonzero potential at the point of zero charge (PZC). Such an effect is outside the popular Gouy-Chapman theory, although it can be introduced. It arises naturally in the mean spherical approximation (MSA). A comparison of the simulation results is made with the linearized modified Gouy-Chapman (LMGC) and MSA. Surprisingly, for monovalent ions, the LMGC theory yields more reliable electrode potentials than does the MSA. In the case when the cations and anions have different charge, a nonzero PZC potential results, even if the diameters of the ions are equal. This phenomenon is not reproduced by either of the theories but is predicted by the modified Poisson-Boltzmann (MPB5) theory. Results are presented for the competition of the effects resulting from the size and charge asymmetries of the ions. A comparison of the density and potential profiles, as obtained from MC and LMGC calculations, is reported.