When developing a dynamic system using floating-point arithmetic, you generally do not have to worry about numerical limitations since floating-point data types have high precision and range. Conversely, when working with fixed-point arithmetic, you must consider these factors when developing dynamic systems:
Fixed-point values are rounded. Therefore, the output signal to the plant and the input signal to the control system do not have the same characteristics as the ideal discrete-time signal.
Adding two sufficiently large negative or positive values can produce a result that does not fit into the representation. This will have an adverse effect on the control system.
The accumulated errors that result from the rounding of individual terms within the realization introduce noise into the control signal.
In the ideal system, the output of a stable transfer function (digital filter) approaches some constant for a constant input. With quantization, limit cycles occur where the output oscillates between two values in steady state.
Limitations on precision, effects of rounding and padding
Limitations on range, underflows and overflows, saturation and wrapping
Effects of scaling on fixed-point arithmetic, binary-point only scaling, slope-bias scaling, scaling for speed, and scaling for maximum precision