A data processing apparatus and method are provided for converting an m-bit fixed point number to a rounded floating point number having an n-bit significand, where n is less than m. The data processing apparatus comprises determination logic for determining the bit location of the most significant bit of the value expressed within the m-bit fixed point number, and low order bit analysis logic for determining from a selected number of least significant bits of the m-bit fixed point number a rounding signal indicating whether a rounding increment is required in order to generate the n-bit significand. Generation logic is then arranged in response to the rounding signal to generate a rounding bit sequence appropriate having regard to the bit location determined by the determination logic. Adder logic then adds the rounding bit sequence to the m-bit fixed point number to generate an intermediate result, whereafter normalisation logic shifts the intermediate result to generate the n-bit significand. At this point, due to the incorporation of the rounding information prior to the addition, the generated n-bit significand is correctly rounded.