IEEE floating-point arithmetic standards 754 and 854 reflect the present state of the art in designing and implementing floating-point arithmetic units. A formalism applied to a standard non-trapping mode floating-point system shows incorrectness of some numeric and non-numeric results. A software emulation of decimal floating-point computer arithmetic supporting an enhanced set of exception symbols is reported. Some implementation details, discussion of some open questions about utility and consistency of the implemented arithmetic with the IEEE Standards are provided. The potential benefit for computations with infinite symbolic elements is outlined.