Digital Arithmetic
Binary representations of fractional numbers allow processors to execute high-dynamic-range mathematical operations. In embedded sensors, floating point calculation enables the direct conversion of raw analog voltage readings into physical units. The hardware processes these values using exponent and mantissa subdivisions.
This approach eliminates the scaling restrictions inherent to fixed-point integers.
Precision Limitation
Numerical rounding occurs when fractional values cannot be represented exactly in binary format. In a typical floating point calculation, this quantization error introduces a tiny but cumulative noise floor during long measurement runs. High-resolution instrumentation must use double-precision variables to maintain measurement accuracy.
Metrological Bias
Accumulating errors in iterative algorithms can drift the zero point of a sensor over long-term operations. To prevent this drift, a floating point calculation must be designed to avoid subtracting two nearly equal large numbers. This subtractive cancellation can destroy the accuracy of statistical variances and averages.
It is avoided by utilizing compensated summation techniques.
Firmware Implementation
Embedded processors without dedicated hardware coprocessors perform numerical operations through software emulation. When implementing floating point calculation in a microcontroller, execution speed can become a bottle-neck for high-frequency data acquisition. System designers must verify that the math execution time does not exceed the sampling period.
If the execution is too slow, the processor will miss data packets, resulting in sample loss and inaccurate signal reconstruction.
