A system for converting digital signals into analog signals using sigma-delta modulation and includes a signed thermometer encoder for converting a plurality of signed binary data received at the encoder into a plurality of signed thermometer data and a rotational dynamic element matching (DEM) arrangement for receiving the plurality of signed binary data and the plurality of signed thermometer data. The rotational DEM arrangement further includes a first barrel shifter for receiving a positive thermometer data at a cycle, the first barrel shifter having a first pointer indicating a starting position of next positive thermometer data, and a second barrel shifter for receiving a negative thermometer data at a cycle, the second shifter having a second pointer indicating a starting position of next negative thermometer data, wherein the first pointer is circularly shifted as a function of positive binary data and the second pointer is circularly shifted as a function of negative binary data.