Question

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How to convert floats to human-readable fractions?

I have a floating point value say 0.595781 which I would like to get as close to as possible using a quotient that uses only integer numerator and denominator values which are both limited in range from 0 to 1023 (10-bits).

The intuitive way to do this (at least to start off) would be use 595/1000 which provides 0.555 a fairly close match (the error is 0.040781).

But there is a better match of 597/1002 which is 0.595808 (an error of 0.0000273). There may be better matches also. I came to the second quotient by playing about with the numerator and denominator values close to their original values in an irrerative way.

I then wondered if there was a way given all the criteria to get the numerator and denominator integer values directly.

In case your wondering the two integer values are required to setup the baud rate generator for an Infineon XE167G device.

Any ideas would be appreciated.
Regards

Answer 1

If you are using 16-bit integers, you could just have numerator = 59578 and denominator just hold a power factor of 10, for instance 5. So the answer would be 59578/(10^5).

With this approach you would at least keep 4 places of precision.
Just a thought…