How can I convert this number representation to a float?

Question

I read this 16-bit value from a temperature sensor (type MCP9808)

Ignoring the first three MSBs, what's an easy way to convert the other bits to a float? I managed to convert the values 2^7 through 2^0 to an integer with some bit-shifting:

uint16_t rawBits = readSensor();
int16_t value = (rawBits << 3) / 128;

However I can't think of an easy way to also include the bits with an exponent smaller than 0, except for manually checking if they're set and then adding 1/2, 1/4, 1/8 and 1/16 to the result respectively.

Answer 1

Something like this seems pretty reasonable. Take the number portion, divide by 16, and fix the sign.

float tempSensor(uint16_t value) {
  bool negative = (value & 0x1000);
  return (negative ? -1 : 1) * (value & 0x0FFF) / 16.0f;
}