A value V is to be rounded to an arbitrary precision resulting in the value V". Conventional rounding technique uses one step to accomplish this. Multistep rounding uses several steps to round the value V to successively shorter precisions with the final rounding step producing the desired value V". This alternate rounding method is one way to implement with the minimum of hardware, the denormalization process that the IEEE Floating-Point Standard 754 requires when underflow occurs. There are certain cases for which multistep rounding produces a different result than single-step rounding. To prevent such a step error, the author introduces a rounding procedure called gradual rounding that is very similar to conventional rounding with the addition of two tag bits associated with each floating-point register.>