Htydjtk

On a custom board I have an ADC which measures -5V to +5V. And outputs in Hex via SPI like this:

0x8000 to 0x0000 = most negative to 0

0x0000 to 0x7FFF = 0 to most positive

I just started studiyng ADCs so I am not sure what is going on. I beleive I have negative full scale of -5V and positive full scale of +5V.

Questions:

• What this numbering system is based on? Is it two's complement?


• Why there is no 0xFFFF value?


• How can I convert these numbers to a real voltage?

It looks like you have a 16-bit, 2's-complement ADC with a range of $-5V le V_{IN} < 5V$. If that's the case, then the digital values can be interpreted as signed integers from -32768 to +32767. The measured voltage is

$ V_{IN} = frac{DigitalValue}{32768} times 5$

If you count most negative to 0 using integers, you count ..., -4, -3, -2, -1, 0
If you count most negative to 0 using hexadecimals, you count (in your case) 0x8000, 0x8001 ..., 0xFFFE, 0xFFFF, 0

So, there is the 0xFFFF.

Now, your scale is 0X8000 to 0x7FFF, so, in decimal -32768 to 32767, the full scale is 65636 (-32768 +-32767 + 1). The scale represents -5V to +5V, full scale 10V.
The conversion is:

Vmeasured = SPI_OUPUT_in_HEX / 65536 * 10V

P.S. I guess using 65536 or 65535 for dividing is a matter of taste; it hardly influences the accuracy. Using 65535 may be preferable/nessecary in old tiny microprocessors.

I'll just add to @Eliot's answer that in reality if you have floating point math available (and choose to use it) you should convert DigitalValue to floating point before dividing.

If you only have integer math available you can multiply by five (you need more than 16 bits, obviously) and then throw away the least-significant 2 bits (or round) and place the radix point right of the 4th bit. For example 0x7FFF FFFF -> 0x27FF FFFF FB -> 0x4.FFF FFFF (one LSB less than 5.0000).

Recommended thing would be to grab datasheet for your ADC chip and see in chapter named "Data Format". In this chapter it will be explained how the numeric values (data) from the ADC is represented.

It seems that your digital representation is something named 2's complement. Here is the wiki link.

From values you have provided I assume it is 16-bit ADC. So, max value 0x7FFF is your +Vref (positive reference voltage) and 0x8000 is -Vref (negative reference voltage).

Example:

Let's say your positive reference voltage is 2.5V, and negative reference voltage is -2.5V, then when you see obtained value of ADC equal 0x7FFF it means you have 2.5V on the ADC input. To calculate other positive values you take Vref and divide it by numbers of bits value (0x7FFF equals to dec 32767), so if your ADC gives you 0x0001 is equivalent of 2.5[V]/32767 = 0.000076[V]
For negative numbers: if your ADC value is bigger or equal to 0x7FFF then your action may be: negative_measured_value = measured_value - (0xFFFF + 1)

So, when ADC provides you value of 0xFFFF it goes:

negative_measured_value = 0xFFFF - (0xFFFF +1) = -1

true_volt_value = -1 * (2.5[V]/32767) = -0.000076V

Huisman answers it as well.