  The presence of excess emission at 3.6--8.0 $\mu$m was investigated in a
sample of 27 binary systems located in two nearby star-forming regions, Taurus
and Ophiuchus, by using Spitzer/Infrared Array Camera (IRAC) archival data.
Angular (Projected) separations for the binaries are greater than 2"($\sim$280
AU), which allowed us to perform spatially resolved photometry of individual
primary and secondary sources. The measured occurrence of infrared excess
suggests that binarity plays a role in the evolution of circumstellar disks,
even at such wide binary separations. Most of the binaries have excess emission
from both the circumprimary and circumsecondary disks, or show photospheric
levels for both components at all four wavelengths of IRAC. On the other hand,
four systems ($17^{+11}_{-8}$%, designated by "mixed" systems) exhibit excess
emission from a single binary component. This ratio is significantly smaller
than that predicted by the random pairing of single stars, suggesting that
circumprimary and circumsecondary disks are synchronously dispersed. In
addition, the excess frequencies (EFs) of primary and secondary sources with a
projected distance of $a_{\rm p}$$\simeq$280--450 AU are $100^{+0}_{-17}$% and
$91^{+8}_{-18}$%, respectively, and significantly higher than that of single
stars ($70 \pm 5$%). We made a simple model describing the EF distribution as a
function of the disk outer radius, $R_{\rm out}$. Comparisons with observations
using the Kolmogorov-Smirnov test show that the observational data are
consistent with the model when the $\rm{EF} \simeq 1$ region is found at
$R_{\rm out}$$\sim$30--100 AU. This disk radius is smaller than that typically
estimated for single stars. The high EF of circumstellar disks with these radii
may indicate a prolonged lifetime of dust in binary systems possibly because
smaller disks counteract mass loss by photoevaporation.
