A DPCM operation which can reduce the size of differential data and a method and an apparatus for encoding data using the DPCM operation are provided. A method for generating differential data includes generating differential data by performing a DPCM operation on quantized data and generating predicted differential data by performing a predicted DPCM operation on the quantized data, generating circular-quantized differential data and circular-quantized predicted differential data by performing a circular quantization operation on the differential data and the predicted differential data so as to reduce their ranges, and selecting one of the circular-quantized differential data and the circular-quantized predicted differential data depending on their magnitudes.