A data processing apparatus and method are provided for normalizing a data value to produce a result value. The data processing apparatus includes prediction logic for generating a shift indication based on a prediction of the number of bit positions by which the data value needs to be shifted in order to normalize the data value. Further, normalizer logic is used to apply a shift operation to the data value based on the shift indication. In addition, correction logic is operable in parallel with the normalizer logic to determine from the data value and a least significant bit of the shift indication whether the shift indication has correctly predicted the number of bit positions by which the data value needs to be shifted in order to normalize the data value, or whether instead the prediction is incorrect, and to generate an output signal dependent on that determination. Shift logic is then used, if the output signal indicates that the prediction is incorrect, to apply a correction shift such that the result value is the normalized data value.