  We investigate the ground-state properties of two-component Bose gases
confined in one-dimensional harmonic traps in the scheme of density-functional
theory. The density-functional calculations employ a Bethe-ansatz-based
local-density approximation for the correlation energy, which accounts for the
correlation effect properly in the full physical regime. For the binary Bose
mixture with spin-independent interaction, the homogeneous reference system is
exactly solvable by the Bethe-ansatz method. Within the local-density
approximation, we determine the density distribution of each component and
study its evolution from Bose distributions to Fermi-like distribution with the
increase in interaction. For the binary mixture of Tonks-Girardeau gases with a
tunable inter-species repulsion, with a generalized Bose-Fermi transformation
we show that the Bose mixture can be mapped into a two-component Fermi gas,
which corresponds to exact soluble Yang-Gaudin model for the homogeneous
system. Based on the ground-state energy function of the Yang-Gaudin model, the
ground-state density distributions are calculated for various inter-species
interactions. It is shown that with the increase in inter-species interaction,
the system exhibits composite-fermionization crossover.
