The ADC translates an analog input signal to a digital output value representing the size of the input relative to a reference. To get a better basis for describing a general ADC, this document distinguishes between ideal, perfect, and actual ADCs.
An ideal ADC is just a theoretical concept, and cannot be implemented in real life. It has infinite resolution, where every possible input value gives a unique output from the ADC within the specified conversion range. An ideal ADC can be described mathematically by a straight-line transfer function, as shown in the figure below.
To define a perfect ADC, the concept of quantization must be introduced. Due to the digital nature of an ADC, continuous output values are not possible. The output range must be divided into a number of steps, one for each possible digital output value. This means that one output value does not correspond to a unique input value, but a small range of input values. This results in a staircase transfer function. The resolution of the ADC equals the number of unique output values. For instance, an ADC with eight output steps has a resolution of eight levels or, in other words, three bits. The transfer function of an example 3-bit perfect ADC is shown in the figure below together with the transfer function of an ideal ADC. As seen on the figure, the perfect ADC equals the ideal ADC on the exact midpoint of every step. This means that the perfect ADC essentially rounds input values to the nearest output step value.
The maximum error for a perfect ADC is ±½ step. In other words, the maximum quantization error is always ±½ LSB, where LSB is the input voltage difference corresponding to the Least Significant Bit of the output value. Real ADCs have other sources of errors, described later in this document.