The properties of floating point single quantization including under- and overflow

The quantization of floating point numbers is well investigated for situations where no under- or overflow occurs [1-3]. In this paper results are presented including these cases for the quantization of uniform, gaussian and sinusoidal distributed numbers. For underflow two different cases are considered: (1) no unnormalized mantissas occur and numbers whith magnitudes lower than a certain limit are set to zero, (2) unnormalized mantissas are used in the underflow region which leads to a behaviour similar to that of fixed point quantization. It can be seen that different slopes of the SNR vs. S curves in the underflow regions characterize the utilization of normalized or unnormalized mantissas. In the overflow-region it is assumed that saturation is utilized, which means that numbers with magnitude greater than a certain limit are set to fixed overflow values.