The operation of a first-order 2-bit adaptive sigma-delta modulation system is described and discussed in this paper. The system operation is based on the combination of both "memory" and "look-ahead" estimation in the employed step-size adaptation algorithm of the basic quantizer. In comparison to simple systems and other adaptive sigma-delta systems, computer simulation results show that these features of the described system are responsible for the high SNR values and the extended dynamic range achieved for AC signals as well as the noise power reduction of almost 10 dB and the complete elimination of the idle tones for DC signals. However, such an advantageous performance requires the least possible multiplicative error accumulation, and this cannot be achieved without analog circuits of the highest possible accuracy.