An improved dynamic element matching technique for providing noise-shaping of non-linearity in data converters, such as a multi-bit digital-to-analog converter, is provided. The improved DEM technique is configured with a new method for generating the bit patterns, which permits a less complex digital DEM circuit that provides improved performance. The proposed DEM algorithm introduces a new priority calculation method in which a multi-bit quantizer can be used in an oversampled delta sigma modulator to produce an output which is converted to an output code, such as a thermometer code output. The thermometer code output can be coupled as input bits through a dynamic element matching sort block to provide an output comprising a plurality of bits. Each output bit of the dynamic element matching sort block is sampled and coupled back to each of a plurality of corresponding filters, which comprise cascaded integrators. The sort block is configured to compare the respective outputs of each filter to shuffle the input bits to generate an output such that the filter output values converge towards each other. In this way, the bit sequence on each output bit line will have the noise-shaping with the order determined by the number of integrators cascaded in the signal path of each filter. The resultant output signals can then be passed through an internal multi-bit DAC to provide an output to an analog low-pass filter to remove out-of-band noise, leaving the signal band having an improved signal-to-noise (SNR) with the non-linearity components removed.