We fabricated highly doped Si single-electron transistors (SETs) with a series of geometrically defined islands. The conduction mechanism was systematically investigated in the temperature range from 4.2 K to 100 K. Despite their island size variation, some of the SETs showed clear periodic and quasiperiodic Coulomb oscillations. This is in contrast to the conventional idea that only geometrically uniform islands show periodic Coulomb oscillations. We showed theoretically that periodic Coulomb oscillation appears under the small deviation of gate capacitances with the period determined by the average of the capacitances. We also found that the formed charge soliton that was conducted through the islands was spread over the whole array. This may also contribute to the periodicity of the Coulomb oscillation. The SET with multiple islands was applied to an Exclusive-OR circuit and achieved a room temperature operation.