Linear Circuit Design Handbook

The four primary DC errors in a data converter are offset error, gain error, and two types of linearity error (differential and integral). Offset and gain errors are analogous to offset and gain errors in amplifiers as shown in Figure 6-113 for a bipolar input range. (Though offset error and zero error, which are identical in amplifiers and unipolar data converters, are not identical in bipolar converters and should be carefully distinguished.)
The transfer characteristics of both DACs and ADCs may be expressed as D = K + GA, where D is the digital code, A is the analog signal, and K and G are constants. In a unipolar converter, K is zero, and in an offset bipolar converter, it is ?1 MSB. The offset error is the amount by which the actual value of K differs from its ideal value.
The gain error is the amount by which G differs from its ideal value, and is generally expressed as the percentage difference between the two, although it may be defined as the gain error contribution (in millivolt or LSB) to the total error at full-scale. These errors can usually be trimmed by the data converter user. Note, however, that amplifier offset is trimmed at zero input, and then the gain is trimmed near to full-scale. The trim algorithm for a bipolar data converter is not so straightforward.