This bit to measurement resolution converter will calculate the reading resolution of a digital measurement device and display the answer in number of steps, percentage of full span, parts per million and decimal ratio.
Description of Terms
Number of Bits
Select the number of bits specified for the microprocessor, digital to analog converter or analog to digital converter for which you wish to determine the measurement resolution.
Resolution Calculation Method
Two methods are used to determine the resolution of digital measurement devices such as digital to analog converters or analog to digital converters. One method is R = 2n and the other is R = 2n – 1, the former determines the number of discreet digital values and the latter the number of divisions between each discreet value. e.g. a 2 bit ADC would output 4 possible values 0, 1, 10, 11, whereas a 2 bit DAC would produce a 3 stepped output.
The maximum number of discreet values or divisions that it is possible to produce from the selected number of bits.
Full Span Percentage
The minimum possible proportion expressed as a percentage of the available range that can be measured. This is calculated by dividing one hundred by the number of steps, or 100/steps.
Parts per Million (PPM)
The smallest possible difference in values that can be measured, if compared to a scale of 0 to 1,000,000. This is calculated by dividing one million by the number of steps, or 1000000/steps.
Decimal Ratio Proportion
This represents the minimum fraction of the device range that can be measured. This calculated by dividing one by the number of steps, or 1/steps.
What is a bit?
A bit is number which uses a Base one numbering systems more commonly known as a binary number, and it can have the value of 0 or 1. For example a 12 bit number would be 12 digits long with each digital being a 0 or 1.
How does the number of bits relate directly to measurement resolution?
The number of bits that I device can handle tells signifies the maximum possible number of discreet values that can be determined over a range of measurement.
For example a 12 bit DAC (digital to analogue converter) will convert a digital value into an analogue signal such as 0 to 10 volts dc. To calculate the number of discreet values or amount of steps that the 0-10Vdc output can be incremented by, you would multiply 2 by itself as many times as there are bits. i.e. 2n where n = number of bits.
The number 2 is used because each bit has a possibility of 2 values of 0 or 1. Therefore if you had a 2 bit device it would provide 4 possible values 0, 1, 10 or 11. So in this case the resolution would be 1:4 or 25% since it is not possible to discern a value of less than 25% of the range. If you had 3 bit device there would be 8 possible values, therefore the resolution would be 1:8 or 12.5% which is twice as good as the 2 bit device. Each extra bit directly relates to a doubling of the measurement resolution.