  Binary stars play a vital role in astrophysical research, as a good fraction
of stars are in binaries. Binary fraction (BF) is known to change with stellar
mass in the Galactic field, but such studies in clusters require binary
identification and membership information. Here, we estimate the total and
spectral-type-wise high mass-ratio (HMR) BF ($f^{0.6}$) in 23 open clusters
using unresolved binaries in color-magnitude diagrams using \textit{Gaia} DR2
data. We introduce the segregation index (SI) parameter to trace mass
segregation of HMR (total and mass-wise) binaries and the reference population.
This study finds that in open clusters, (1) HMR BF for the mass range 0.4--3.6
Msun (early M to late B type) has a range of 0.12 to 0.38 with a peak at
0.12--0.20, (2) older clusters have a relatively higher HMR BF, (3) the
mass-ratio distribution is unlikely to be a flat distribution and BF(total)
$\sim$ (1.5 to 2.5) $\times f^{0.6}$, (4) a decreasing BF(total) from late
B-type to K-type, in agreement with the Galactic field stars, (5) older
clusters show radial segregation of HMR binaries, (6) B and A/F type HMR
binaries show radial segregation in some young clusters suggesting a primordial
origin. This study will constrain the initial conditions and identify the major
mechanisms that regulate binary formation in clusters. Primordial segregation
of HMR binaries could result from massive clumps spatially segregated in the
collapse phase of the molecular cloud.
