A floating point unit, a central processing unit, and a method are provided for adjusting the exponent of a floating point number. During an addition or subtraction of two floating point numbers, the significand of the floating point result is rounded, and the exponent of the result may be adjusted due to normalization or renormalization. The exponent adjustment due to renormalization or the exponent adjustment due to normalization and renormalization is combined with the significand rounding operation.