  Fragmentation and binary formation processes are studied using
three-dimensional resistive MHD nested grid simulations. Starting with a
Bonnor-Ebert isothermal cloud rotating in a uniform magnetic field, we
calculate the cloud evolution from the molecular cloud core (n=10^4 cm^-3) to
the stellar core (n \simeq 10^22 cm^-3). We calculated 147 models with
different initial magnetic, rotational, and thermal energies, and the
amplitudes of the non-axisymmetric perturbation. In a collapsing cloud,
fragmentation is mainly controlled by the initial ratio of the rotational to
the magnetic energy, regardless of the initial thermal energy and amplitude of
the non-axisymmetric perturbation. When the clouds have large rotational
energies in relation to magnetic energies, fragmentation occurs in the
low-density evolution phase (10^12 cm^-3 < n < 10^15 cm^-3) with separations of
3-300 AU. Fragments that appeared in this phase are expected to evolve into
wide binary systems. On the other hand, fragmentation does not occur in the
low-density evolution phase, when initial clouds have large magnetic energies
in relation to the rotational energies. In these clouds, fragmentation only
occurs in the high-density evolution phase (n > 10^17 cm^-3) after the clouds
experience significant reduction of the magnetic field owing to Ohmic
dissipation in the period of 10^12 cm^-3 < n < 10^15 cm^-3. Fragments appearing
in this phase have separations of < 0.3 AU, and are expected to evolve into
close binary systems. As a result, we found two typical fragmentation epochs,
which cause different stellar separations. Although these typical separations
are disturbed in the subsequent gas accretion phase, we might be able to
observe two peaks of binary separations in extremely young stellar groups.
