All-electron first-principles total energy electronic structure calculations were carried out for single chains of four nucleotide base stacks (composed of adenine, thymine, guanine, and cytosine, respectively) in the DNA B conformation (3.36 Angstrom stacking distance and 36 degrees screw angle theta) using the local-density approximation (LDA) within a helical band structure approach. A uracil stack was also computed in the DNA B conformation and compared with the results obtained for the four DNA base stacks. The total energies per unit cell as a function of the stacking distance (at fixed screw angle theta = 36 degrees) and of the screw angle (at d = 3.36 Angstrom) show in most cases rather good agreement with the experiment. As expected with LDA calculations, the band gaps were underestimated by nearly 50% compared to experimentally suggested values. Finally, some suggestions are given for the improvement of the band structures of the nucleotide base stacks.