The top equation here is the same equation as given before that expresses the output current for an ideal current-output DAC. Of course, a real DAC is not perfect and introduces errors resulting in a deviation from this ideal expression. The errors can be thought of as a small deviation in output current for each input code. This is modeled by the term, i subscript x, in the second equation. That is, i subscript x is the error current associated with a particular code, x, and varies from code to code. Ideally, the DAC output should be a perfectly linear function of the input code, x. This can be seen in the form of the first equation, which is the equation of a line with slope given by the quantity (Imax minus Imin) divided by the quantity 2 to the D minus 1. In the second equation, however, the inclusion of the term, i subscript x, results in a deviation from perfect linearity because it differs for each input value, x. Most DAC datasheets provide a measure of the effect of this error term. One measure of the i subscript x error term is differential nonlinearity, or DNL. It is the amount by which the output changes for an input change of one step (or LSB) minus the ideal output step size. DNL is measured for each pair of adjacent input codes over the entire input range. The unit of measure is the nominal change in output for a 1 LSB input change, that is, the measurement is given in LSB units. In a datasheet, DNL is usually reported as a single number representing the magnitude of the largest DNL value that appears over the entire input range. The other measure of the affect of the i subscript x error term is integrated nonlinearity, or INL. It is a measure of the accumulation of DNL values. It, too, is measured in LSB units. If the DNL values are randomly distributed with 0-mean, then their accumulation would be 0, yielding an INL of 0. Oftentimes, however, DNL values have a deterministic component that is not completely random resulting in a non-zero accumulation and a non-zero INL value. Like DNL, INL appears on datasheets as a single value denoting the largest accumulated magnitude of the entire input range. INL tends to indicate that the input to output relationship of the DAC is not perfectly linear, but is warped or bowed. DNL and INL affect the DAC output spectrum differently. DNL with a 0-mean distribution tends to add to the noise floor of the output spectrum without any significant spurious effects. On the other hand, the existence of INL implies a non-0-mean DNL, which implies a nonlinear input-output relationship. The result is the appearance of harmonic spurs in the output spectrum as opposed to an increase in the noise floor.