Understanding the resolution of the DS18B20 - mismatch between specs?

Question

I am interested in the DS18B20 temperature sensor from Maxim Integrated. The datasheet is here:

https://datasheets.maximintegrated.com/en/ds/DS18B20.pdf

The datasheet mentions:

• "Measures Temperatures from -55°C to +125°C"
• "The resolution of the temperature sensor is user-configurable to 9, 10, 11, or 12 bits, corresponding to increments of 0.5°C, 0.25°C, 0.125°C, and 0.0625°C, respectively."

But when I compute this by hand, I get that, at 12 bits resolution, between -55 and +125 degrees, the resolution in degrees celcius "should" be:

(125+55) / (2**12) = 0.044

(using 2 significant digits).

How to understand the mismatch? Does that mean that only "part of" the 12 bits resolution is really used? Then I guess it is not strictly speaking "12 bits resolution", right?

Answer 1

If you look at the DS18B20 datasheet, page 6 you can see that it does not use the entire range of possible values.

With the maximum resolution (12 bits), it could potentially represent values of -127 to +127 °C (7 bits left of the “binary” point, a sign bit, plus the 1 to 4 fractional bits), of which only the values -55 to +125 are used.

The maximum resolution to the right of the “binary” point is 4 bits, which represents 2^-4 (1/16 = 0.0625 °C).

Answer 2

You calculated your resolution with an assumption that the sensor gives the full temperature range of -55°C to 125°C in full 12-bit code range of between 0 to 4095, or rather, -2048 to +2047, but it doesn't.

The chip is just guaranteed to perform temperature measurements within specifications in the -55°C to +125°C range, which does not tell anything how it represents the measurements in bits.

Since the integer part can be represented in 8 bits, signed 8-bit values can range from -128 to +127, or resolution of 1°C.

• 8 bits : 1/1 = 1.0 °C steps
• 9 bits : 1/2 = 0.5 °C steps
• 10 bits : 1/4 = 0.25 °C steps
• 11 bits : 1/8 = 0.125 °C steps
• 12 bits : 1/16 = 0.0625 °C steps

So the full 12-bit code range can encode range of -2048/16 to 2047/16, or -128.0000 °C to +127.9375 °C.

But only the codes for the range representing -55 to +125 are valid measurements, and codes outside that range are not valid.