Conventional sigma-delta (ΣΔ) analog-to-digital (AD) converters are based on an active analog ΣΔ modulator followed by a digital filter. In earlier papers we proposed a new architecture for a first-order ΣΔ modulator that needs no active analog components. Its advantage is that AD converters can be implemented within FPGAs or directly in the software of microprocessors. Its disadvantage is, however, that it realizes a lossy ΣΔ modulator with an accompanying limited resolution. Here we propose to use dither-injection to relax that resolution limitation and we present simulation results showing that our ideas work.