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A purely digital correction technique combined with data weighted averaging (DWA) algorithm is presented to overcome the digital-to-analog converter's (DAC's) mismatch-induced errors in multibit ΣΔ modulators. This technique needs a foreground calibration process. Simulation results confirm the validity of this combined technique in low oversampling ratios (OSRs). This method enhances the pick signal to noise and distortion ratio (SNDR) about 31.5 dB with respect to the non-calibrated case (1.5 % mismatch) when the OSR is 8.