In-and-out conversions

gy an in-and-out conversion we mean that a floating-point number in one base is converted into a floating-point number in another base and then converted back to a floating-point number in the original base. For all combinations of rounding and truncation conversions the question is considered of how many significant digits are needed in the intermedmte base to allow such in-and-out conversions to return the original number (when possible), or at least to cause a difference of no more than a unit in the least significant digit.