page_title: Analog-to-digital converter
section_title: Resolution
hierarchical_section_title: Analog-to-digital converter / Explanation / Resolution
context_page_description: In electronics, an analog-to-digital converter is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an input analog voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities.
  There are several ADC architectures. Due to the complexity and the need for precisely matched components, all but the most specialized ADCs are implemented as integrated circuits. These typically take the form of metal–oxide–semiconductor mixed-signal integrated circuit chips that integrate both analog and digital circuits.
  A digital-to-analog converter performs the reverse function; it converts a digital signal into an analog signal.
context_section_description: The resolution of the converter indicates the number of different, ie discrete, values it can produce over the allowed range of analog input values. Thus a particular resolution determines the magnitude of the quantization error and therefore determines the maximum possible  signal-to-noise ratio for an ideal ADC without the use of oversampling.  The input samples are usually stored electronically in binary form within the ADC, so the resolution is usually expressed as the audio bit depth. In consequence, the number of discrete values available is usually a power of two. For example, an ADC with a resolution of 8 bits can encode an analog input to one in 256 different levels (2⁸ = 256). The values can represent the ranges from 0 to 255 (i.e. as unsigned integers) or from −128 to 127 (i.e. as signed integer), depending on the application.
  Resolution can also be defined electrically, and expressed in volts. The change in voltage required to guarantee a change in the output code level is called the least significant bit (LSB) voltage. The resolution Q of the ADC is equal to the LSB voltage. The voltage resolution of an ADC is equal to its overall voltage measurement range divided by the  number of intervals:
  where M is the ADC's resolution in bits and EFSR is the full scale voltage range (also called 'span'). EFSR is given by
  where VRefHi and VRefLow are the upper and lower extremes, respectively, of the voltages that can be coded.
  Normally, the number of voltage intervals is given by
  where M is the ADC's resolution in bits.
  That is, one voltage interval is assigned in between two consecutive code levels.
  Example:
  Coding scheme as in figure 1
  Full scale measurement range = 0 to 1 volt
  ADC resolution is 3 bits: 2³ = 8 quantization levels (codes)
  ADC voltage resolution, Q = 1 V / 8 = 0.125 V.
  In many cases, the useful resolution of a converter is limited by the signal-to-noise ratio (SNR) and other errors in the overall system expressed as an ENOB.
caption: Fig. 1. An 8-level ADC coding scheme.