The electrical resistivity and the Hall effect have been measured on oriented single crystals of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{4}$${\mathrm{O}}_{8}$ in magnetic fields up to 10 T and temperatures from 2 to 300 K. In the normal state the anisotropic, transverse relaxation rates determined from the Hall angle for I\ensuremath{\parallel}a and b agree with those obtained from NQR for Cu(2) and Cu(1), respectively, and indicate the formation of a spin gap. In the mixed phase the Hall effect changes its sign twice, but only when I is parallel to the chains. An interpretation in terms of a two-band model is given.