## User Guide

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 = 2^{n} and the other is R = 2^{n} – 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.

#### Division Steps

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 step*s*, 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/step*s*.

#### 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 step*s*, or 1/step*s*.

### FAQs

#### 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. 2^{n} 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.