  We derive and parametrize the Galactic mass function (MF) below 1 $\msol$
characteristic of both single objects and binary systems. We resolve the long
standing discrepancy between the MFs derived from the HST and from the nearby
luminosity functions, respectively. We show that this discrepancy stemmed from
{\it two} cumulative effects, namely (i) incorrect color-magnitude determined
distances, due a substantial fraction of M dwarfs in the HST sample belonging
to the metal-depleted, thick-disk population, as corrected recently by Zheng et
al. and (ii) unresolved binaries. We show that both the nearby and HST MF for
unresolved systems are consistent with a fraction $\sim $50% of M-dwarf
binaries, with the mass of both the primaries and the companions originating
from the same underlying single MF. This implies that $\sim$30% of M dwarfs
should have an M dwarf companion and $\sim$20% should have a brown dwarf
companion, in agreement with recent determinations. The present calculations
show that the so-called "brown-dwarf desert" should be reinterpreted as a lack
of high mass-ratio $(m_2/m_1\la 0.1$) systems, and does not preclude a
substantial fraction of brown dwarfs as companions of M dwarfs or for other
brown dwarfs.
