Calculating the Smallest Detectable Change—Code Width

The resolution and device range of a measurement device determine the smallest detectable change, called the code width, in the input signal. The smaller your code width, the more accurate your measurements are.

You can calculate the code width using the following formula:

code width = device range/ 2^resolution

For example, a 12-bit measurement device with a 0 to 10 V range detects a 2.4 mV change, while the same device with a –10 to 10 V input range detects only a change of 4.8 mV:

device range/ 2^resolution = 10/2¹² = 2.4 mV

device range/ 2^resolution = 20/2¹² = 4.8 mV

A high-resolution A/D converter (ADC) provides a smaller code width given the preceding device voltage ranges.

device range/ 2^resolution = 10/2¹⁶ = 0.15 mV

device range/ 2^resolution = 20/2¹⁶ = 0.3 mV

The following table shows how the code width of a 12-bit measurement device varies by device range. The device selects the best possible range based on the input limits you specify when you create a virtual channel. Select input limits that accurately reflect the signal you want to measure in order to achieve the smallest possible code width. NI-DAQmx coerces those input limits to fit the selected device range.

Overall Device Range	Possible Device Ranges with Gain Adjustment	Precision1
0 to 10 V	0 to 10 V 0 to 5 V 0 to 2.5 V 0 to 1.25 V 0 to 1 V 0 to 0.1 V 0 to 20 mV	2.44 mV 1.22 mV 610 µV 305 µV 244 µV 24.4 µV 4.88 µV
–5 to 5 V	–5 to 5 V –2.5 to 2.5 V –1.25 to 1.25 V –0.625 to 0.625 V –0.5 to 0.5 V –50 to 50 mV –10 to 10 mV	2.44 mV 1.22 mV 610 µV 305 µV 244 µV 24.4 µV 4.88 µV
–10 to 10 V	–10 to 10 V –5 to 5 V –2.5 to 2.5 V –1.25 to 1.25 V –1 to 1 V –0.1 to 0.1 V –20 to 20 mV	4.88 mV 2.44 mV 1.22 mV 610 µV 488 µV 48.8 µV 9.76 µV
1The value of 1 Least Significant Bit (LSB) of the 12-bit ADC. In other words, the voltage increment corresponding to a change of 1 count in the ADC 12-bit count.

Note  The NI 4472 is a 24-bit device with a range of –10 V to 10 V. However, one bit is reserved, leaving an effective resolution of 23 bits. Thus, the code width is 20/223 = 2.38 µV.