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Using the hybrid exchange-correlation functional within the density-functional theory, we have systematically investigated the structural and electronic properties of MO (M = Be, Mg, Ca, Sr, Ba, Zn, Cd) in binary rocksalt (B1), zincblende (B3) and wurtzite (B4) phases, including the structural parameters, bulk moduli, band gaps and deformation potentials. Our results agree well with the experimental data and other theoretical results, and give a better understanding of the relationship between the geometric and electronic structure. After calculating the band alignment, we find that in both the B1 and B3 structures, the valence band maximum (VBM) has an obvious decrease from BeO to MgO to CaO, then it goes up from SrO to BaO to ZnO to CdO. Moreover, the properties of the ternary alloys M$_x$Zn$_{1-x}$O were studied through the application of the special quasirandom structure method. The critical value of the ZnO composition for the transition from the B3 structure to the B1 structure gradually increases from (Ca, Zn)O to (Mg, Zn)O to (Sr, Zn)O to (Ba, Zn)O to (Cd, Zn)O, indicating that (Ca, Zn)O can exist in the B3 structure with the lowest ZnO composition. These results provide a good guideline for the accessible phase space in these alloy systems.