We describe numerical simulations of giant-cell solar convection and magnetic field generation. Nonlinear, three-dimensional, time-dependent solutions of the anelastic magnetohydrodynamic equations are presented for a stratified, rotating, spherical shell of ionized gas. The velocity, magnetic field, and thermodynamic variables are solved simultaneously and self-consistently with full nonlinear feedback. Convection, driven in the outer part of this shell by a superadiabatic gradient, penetrates into the inner, subadiabatic part. Previous dynamic dynamo sjmulations have demonstrated that, when the dynamo operates in the convection zone, the magnetic fields propagate away from the equator in the opposite direction inferred from the solar butterfly diagram. Our simulations suggest that the solar dynamo may be operating at the base of the convection zone in the transition region between the stable interior and the turbulent convective region. There our simulated angular velocity decreases with depth, as it does in the convection zone; but the simulated helicity has the opposite sign compared to its convection zone value. As a result, our simulated magnetic fields in this transition region initially propagated toward the equator. However, due to our limited numerical resolution of the small amplitude helical fluid motions in this dense, stable region, only the initial phase propagation could be simulated, not a complete magnetic cycle.