A system for handling denormal floating point operands when the result must be normalized. A leading zero counter (lzc) on the operand B (opB) is used to limit alignment shifts when opB is denormal but is much greater than the product of operands A and C, i.e. AC. By limiting the additional shift of B during normalization, by the number of leading zeros in opB, no increase is needed in the output bus of the alignment shifter. Furthermore, the additional shift may be done either in the alignment shifter, or postponed to a later stage in the pipeline, where the result is normalized.