An analog to digital converters, or A/D converter, is the reverse system of a D/A converter, which converts an analog signal to its digital form. In my early post we discussed on **how a digital to analog converters works**? Now in this post we will see how an analog to digital converters works? As name suggests we can understand that it will convert analog signal into digital one. So the inputs of this converter will be analog signals and output will be in digital form. In an analog to digital converter, the input analog voltage may have any value in a range and it will produce the digital output of 2^{N} number of discrete values for an N-bit converter. Therefore, the whole range of analog voltage is required to be represented suitably in 2^{N} intervals, and each of the intervals corresponds to a digital output.

Let us take an example, consider that an analog voltage range of 0 to V is represented by 3-bits digital output. As we know that a N-bit system can produce 2^{N} different digital output. So 3-bit digital system can generate 2^{3 }= 8 different digital outputs, the full analog range will be divided into 8 intervals, and each interval of voltage of the size of V/8 is assigned unique digital value. This process is called *quantization*. In bellow figure we will see the interval of analog voltage and their corresponding digital representations.

If we carefully observed the above figure then we can find that a complete voltage interval is represented by a digital value, irrespective of any voltage value within the interval. Therefore, there involves always some error while converting any analog voltage interval to its digital value, which is referred to as *quantization error*.

Again if we concentrate on above figure then we can observed, the voltage interval 0 to 1/8 V is assigned to the digital value 000, voltage interval 1/8 V to 2/8 V is assigned to digital value 001, and so on. Also, it may be noted from the figure that the maximum quantization error is E = 1/8 V. This quantization error may be reduced if the analog voltage interval limits are considered a different way. Let us choose the size of voltage interval as 1/7 V, except the top and bottom intervals which are 1/14 V.