Binary stars can explain the observational CMDs of globular clusters as a whole, but it is clear that
there are some differences between the observational and theoretical CMDs. This possibly results
from the following reasons: Firstly, there are some limitations in our theoretical stellar populations.
For example, the basic inputs (e.g., binary fraction, initial mass function, etc.) of the bsSSP model
remain uncertain and the metallicity intervals are not small enough. Note that the binary fractions
in GCs are possibly lower than those (∼ 50%) in the local fields, open clusters, and star-forming
regions, because frequent dynamical interactions together with binary evolution processes conspire
to effectively destroy binaries in GCs. Secondly, it seems impossible to discriminate every star in
the star clusters, but each star is assumed to be distinguishable in our work because there is no
reliable instruction about how stars in a cluster can be distinguished. This effect is obvious in the low
luminosity part of the main sequences of CMDs. Thirdly, it seems that there are some uncertainties
in the observational CMDs. In addition, the effect of superposition in CMDs has not been taken
into account in this work, thus, this also can considerably affect morphology, especially in crowded
regions such as cluster centers.