Convert Fixed-point to actual value(decimal)

Question

A Microcontroller I have provides Raw data in Fixed-point format Q24 (24bit) by ASIC IC.

I need to convert to decimal by

Actual value = raw_data*LSB

where

LSB = 150/[( (2^24) - 1 )*0.6 ] = 150/10066329 = 1.49011E-5

Range raw data is 0 ~ 10066329

I'd like to calculate Actual value in to uint 32bit and keep the precision in 2 or 3 decimal point.

For example If full scale raw data is 10066329, Actual value with 2 decimal point precision would be 15000 or for 3 decimal point 150000.

I found the way to do this is - Scale factor (but need to reduce the raw data precision for prevent data not over flow in 32 bit) - floating point (make MCU no efficiency)

What option should I select?

I also posted here

Vandhunden Vandhunden · Accepted Answer · 2012-12-08T22:59:42

You can keep full precision and still avoid floating point by using an intermediate 64 bit value:

// raw
unsigned int raw = 10066329;

// conversion
unsigned int actual_a = ((raw >> 6u) * (150000 >> 4u) / 10066329) << 10u;
unsigned int actual_b = (raw * (long long) 150000) / 10066329;

double actual_ref = raw * 150000.0 / 10066329.0;
printf("%.0f\n%u\n%u\n", actual_ref, actual_a, actual_b);

The example above gives the following output (all 32 bit values):

150000    // True value for reference
149504    // Value converted using 32 bit
150000    // Value converted using 64 bit

As you can some precision is lost when you have to truncate the least significant bits of the raw data (this may be perfectly acceptable depending on your application). However, if you use 64 bit, no truncation is needed.

Convert Fixed-point to actual value(decimal)

1 Answers