Convert Raw 14 bit Two's Complement to Signed 16 bit Integer

Question

I am doing some work in embedded C with an accelerometer that returns data as a 14 bit 2\'s complement number. I am storing this result directly into a uint16_t

Answer 1

Converting the 14 bit 2's complement value to 16 bit signed, while maintaining the value is simply a metter of:

int16_t accel = (int16_t)(raw << 2) / 4 ;

The left-shift pushes the sign bit into the 16 bit sign bit position, the divide by four restores the magnitude but maintains its sign. The divide avoids the implementation defined behaviour of an right-shift, but will normally result in a single arithmetic-shift-right on instruction sets that allow. The cast is necessary because raw << 2 is an int expression, and unless int is 16 bit, the divide will simply restore the original value.

It would be simpler however to just shift the accelerometer data left by two bits and treat it as if the sensor was 16 bit in the first place. Normalising everything to 16 bit has the benefit that the code needs no change if you use a sensor with any number of bits up-to 16. The magnitude will simply be four times greater, and the least significant two bits will be zero - no information is gained or lost, and the scaling is arbitrary in any case.

int16_t accel = raw << 2 ;

In both cases, if you want the unsigned magnitude then that is simply:

int32_t mag = (int32_t)labs( (int)accel ) ;