Analog to Digital

Introduction

Analog data is considered 'continuous', and attempts to register all instances of information passed.  Digital data, on the other hand, takes samples of data.  An analog to digital converter (ADC) must take the constant stream of data received from an analog sensor, and allow it to be stored in a finite, digital way. 

A Simplification

Digital data is stored as a collection of 1's and 0's.  A digital input registers only these two types of values.  In a system running on 5V, an input of 5V would correlate to a 1, and 0V is a 0.  You can hopefully see how one might run into an issue when trying to gain more accuracy.  What would a value of 3.72V mean in this scenario?  This is where ADC converters are useful.

Accuracy

Digitally, these values are stored as an array of bits.  Since each bit can hold the value of 0 or 1, 2^n, with n being the number of bits available, represents the accuracy allotted to each value.  If an ADC converter has 8 bits to store information, then its accuracy would be 2^8=256.  Thus there are 256 possible values that can be registered.  If there are 16 bits available, this number jumps to 65 536 possible values.  The level of accuracy depends on the converter being used, and can vary widely.

Conversion

The information is received through voltage.  The analog to digital converter uses a ratio of the voltage received and the voltage passed into the circuit to determine what value should be stored.  Here you will be taken through an example of a circuit that is running 5V, with a 10 bit memory storage giving 2^10=1024 possible values.  The first of these is 0, making the highest value 1023.  Here receiving an input of 5V would result in the storage of the value 1023, and an input of 0V would be 0.  All intermediate values are determined through the ratio seen below:

We can fill in the resolution as the aforementioned 1023, and system voltage as 5V.

Now that we have our equation set up, we can begin to see how the system makes its conversion.  Lets say our ADC receives an input of 2.12V.

Now it is just a matter of solving for x:

Hopefully this example makes it much clearer how this conversion works.  The value will always be stored in a ratio to the total amount of possible values.  If there were 16 bits available, the stored value would be 65 535 / 5.00V * 2.12V = 27 786.  This is obviously much more accurate, but is highly unnecessary in most basic projects, thus 10 bits are often used.

Table of Contents

References