  We present a robust methodology for identifying photometric binaries in star
clusters. Using Gaia DR3, Pan-STARRS and 2MASS data, we self-consistently
define the cluster parameters and binary demographics for the open clusters
(OCs) NGC 2168 (M35), NGC 7789, NGC 6819, NGC 2682 (M67), NGC 188, and NGC
6791. These clusters span in age from ~200 Myr (NGC 2168) to more than ~8 Gyr
(NGC 6791) and have all been extensively studied in the literature. We use the
Bayesian Analysis of Stellar Evolution software suite (BASE-9) to derive the
age, distance, reddening, metallicity, binary fraction, and binary mass-ratio
posterior distributions for each cluster. We perform a careful analysis of our
completeness and also compare our results to previous spectroscopic surveys.
For our sample of main-sequence stars with masses between 0.6 - 1 M_Sun, we
find that these OCs have similar binary fractions that are also broadly
consistent with the field multiplicity fraction. Within the clusters, the
binary fraction increases dramatically toward the cluster centers, likely a
result of mass segregation. Furthermore nearly all clusters show evidence of
mass segregation within the single and binary populations, respectively. The OC
binary fraction increases significantly with cluster age in our sample,
possibly due to a combination of mass-segregation and cluster dissolution
processes. We also find a hint of an anti-correlation between binary fraction
and cluster central density as well as total cluster mass, possibly due to an
increasing frequency of higher energy close stellar encounters that inhibit
long-period binary survival and/or formation.
