A randomized thermometer-coding digital-to-analog converter (DAC) for the reduction of harmonic distortion due to non-ideal circuit mismatch is presented. The present invention introduces a new dynamic element matching technique that contains three properties of randomization, consecutive selection and less element switching activity to achieve good spurious-free dynamic range and small maximum output error. The topology uses a bank of 1-bit DAC elements, whose outputs are summed to produce a multi-level analog output. The binary digital input is encoded to be thermometer code. During a randomization period, the thermometer code is barrel-shifted to a specific starting position where the position is generated randomly. Thus, the DAC noise is randomized with less element switching activity and consecutive selection.