A method is described for improving the dynamic range of A/D and D/A converters. In the case of A/D conversion it consists of an analog preprocessing, an A/D converter of B' bits operating at a high sampling rate f's, followed by a digital postprocessing. This system effectively operates as an A/D converter with B > B' bits with low sampling rate fs. A relation between the required oversampling factor N = f's/fsand the improvement in dynamic range (R = B- B') is derived which indicates that for moderate values of R (3 to 5 bits) the oversampling factor must range from 6-15, which is quite acceptable. The method is also applicable to D/A conversion, but then the pre-processing has to be digital and file postprocessing analog.