A method and system for processing instructions in a floating point unit for executing denormalized numbers in floating point pipeline via serializing uses an instruction unit and having a control unit and a pipelined data flow unit, a shifter and a rounding unit. The floating point unit has an external feedback path for providing intermediate result data from said rounding unit to an input of the pipelined data flow unit to reuse the pipeline for denormalization by passing intermediate results in the pipeline which have a denormalized condition computed after the exponent calculation of the shifting circuit directly from the rounding unit to the top of the dataflow in the pipeline via an external feedback path. The pipelined has two paths which are selected based on the presence of other instructions in the pipeline. If no other instructions are in the pipeline a first path is taken which uses the external feedback path from the rounding unit back into the top of the dataflow. When there are instructions in the pipeline a shifter unit performing normalization of the fraction indicates possible underflow of the exponent, and prepares to hold the exponent and the fraction in a floating point data flow register; and upon detection of exponent underflow during the rounder stage and detection of any other instructions in pipeline; then the control unit forces an interrupt for serialization, and cancels execution of this instruction and other instructions in pipeline.