We investigated the freezing of equi-concentration binary hard or soft sphere mixtures for various size ratios, sigma (2)/sigma (1), using density functional theory. The Grand Potential is minimized using an unbiased, discrete, real-space mesh that does not constrain the shape of the density, and, in many cases, leads to solutions qualitatively different from those using Gaussians and plane-waves. Besides the usual face-centered-cubic solid-solution phase for sigma (2)/sigma (1) approximate to 1.0, we find a sublattice-melt phase for sigma (2)/sigma (1) = 0.85-0.5 (where the small-sphere density is nonlocalized and multi-peaked) and the NaCl phase for sigma (2)/sigma (1) = 0.45-0.35 (when the small-sphere density again sharpens). For a range of size ratios of soft sphere mixtures, we could not find stable nonuniform solutions. Preliminary calculations within a Modified-Weighted Density-Approximation suggest that such multiple-peaked solutions are not unique to a particular density functional theory.