A pipelined data unit for use in a data processor, the data unit having special input operand check logic for involking a precise exception handling mechanism if either or both of the input operands fails the check, and output result format logic for involking an imprecise exception handling mechanism if the output result cannot be provided in a selected format. Special buffers are also provided to allow the control and status information unique to each instruction to flow through the pipeline together with that instruction. Sufficient information relating to each instruction being executed in the data unit is retained and made readily available to the handlers, so that each type of exception may be handled, should recovery be possible.