||We use the t-t'- U model as a model for the normal states of the electron and hole doped high temperature superconductors. We solve this model on a 4 x 4 square lattice using exact diagonalizat ion. We focus on two controversial issues: the possibility of phase separation and the validity of the rigid band approximation for both hole doped and electron doped system. To study the possibility of phase separation, we calculate the binding energies of carrier clusters as well as the chemical potentials at different carrier concentrations. For the hole doped system, evidence of phase separation is found in the strong coupling regime, but not in the intermediate coupling regime. For electron doped system, tendency towards carrier pairing instead of phase separation is found. To study the validity of the rigid band approximation, we calculate the momentum distributions and the spectral functions. We find that the rigid band filling picture describes the electron doped system well. For the hole doped system, redistribution of particle density in momentum space occurs on doping. This implies that many body effect is significant and the rigid band filling picture may not be valid in the hole doped system.