Multiferroics are singular materials that can exhibit simultaneously electric and magnetic orders. Some are ferroelectric and ferromagnetic and provide the opportunity to encode information in electric polarization and magnetization to obtain four logic states. However, such materials are rare and schemes allowing a simple electrical readout of these states have not been demonstrated in the same device. Here, we show that films of La0.1Bi0.9MnO3 (LBMO) are ferromagnetic and ferroelectric, and retain both ferroic properties down to a thickness of 2 nm. We have integrated such ultrathin multiferroic films as barriers in spin-filter-type tunnel junctions that exploit the magnetic and ferroelectric degrees of freedom of LBMO. Whereas ferromagnetism permits read operations reminiscent of magnetic random access memories (MRAM), the electrical switching evokes a ferroelectric RAM write operation. Significantly, our device does not require the destructive ferroelectric readout, and therefore represents an advance over the original four-state memory concept based on multiferroics.