Bluetooth Floating Point representation

Question

I'm trying to implement this Bluetooth mesh characteristic:

<!--
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-->
<Characteristic xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="http://schemas.bluetooth.org/Documents/characteristic.xsd" name="Illuminance" type="org.bluetooth.characteristic.illuminance" uuid="2AFB" last-modified="2017-07-11" approved="Yes">
  <InformativeText>
    <Abstract>
    The Illuminance characteristic is used to represent a measure of illuminance in units of lux.
    </Abstract>
  </InformativeText>
  <Value>
    <Field name="Illuminance">
      <InformativeText>Unit is lux with a resolution of 0.01.</InformativeText>
      <Format>uint24</Format>
      <Unit>org.bluetooth.unit.lux</Unit>
      <Minimum>0</Minimum>
      <Maximum>167772.14</Maximum>
      <DecimalExponent>-2</DecimalExponent>
      <BinaryExponent>0</BinaryExponent>
      <Multipler>1</Multipler>
      <Description>
        A value of 0xFFFFFF represents 'value is not known'. All other values are Prohibited.
      </Description>
    </Field>
  </Value>
</Characteristic>

https://www.bluetooth.com/wp-content/uploads/Sitecore-Media-Library/Specifications/Mesh/Xml/Characteristics/org.bluetooth.characteristic.illuminance.xml. This characteristic represents a lux value in 3 bytes.

But I don't know how I would be able to convert a value like 0x123456 to the real floating-point number. It doesn't seem that the standard IEEE 754 standard is used. I also don't know what they mean with DecimalExponent and BinaryExponent.

Could anyone help me out? Kind regards, Daan

Answer 1

There is no floating point in the page you link to. It uses -2 with DecimalExponent merely to specify that a 24-bit integer value that in plain binary would be some number x from 0 to 16,777,214 (with 16,777,215 reserved for “not known”) represents a value of x•10⁻² lux, ranging from 0.00 lux to 167,772.14 lux. This is fixed point, not floating point; the point is fixed at the position two digits to the left of where it would be in the plain binary integer representation.