The binary properties of open clusters place crucial constraints on star formation theory and cluster dynamical evolution. We build a comprehensive Bayesian framework that models the color-magnitude diagram (CMD) of a cluster as the mixture of single stars and photometric unresolved binaries. This framework enables us to infer the concerned cluster properties with high accuracy and precision, in particular, the binary fraction $f_b$ and binary mass-ratio index $\gamma_q$, which were unfeasible using conventional methods. As the first example, we apply the method to NGC3532 with Gaia DR2 photometry. Since the binary fraction estimate is sensitive to the exact location and width of the main sequence, we determine the main sequence ridge line with a modified Gaussian process and estimate its scatter from the observed CMD as model input. We obtain $f_b=0.267\pm0.019$ and $\gamma_q=-0.10\pm0.22$ for binaries with mass ratio $q>0.2$ and major mass 0.5 -- 1.5$M_\odot$. A $\gamma_q$ close to zero implies the mass ratios of binaries follow a nearly uniform distribution. Further dividing NGC3532 into subsamples, for the first time in observation, we show that the stars with smaller mass or in the inner region tend to have lower $f_b$ and smaller $\gamma_q$ due to the lack of low mass-ratio binaries. The clear dependence of binary properties on mass and radius is most likely caused by the internal dynamics. Binaries with smaller primary mass or lower mass-ratio have smaller binding energy; hence are more vulnerable to dynamical disruption, especially in the inner region where stars interact more frequently.
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