An analog-to-digital converter converts real-world continuous analog signals into symbolic discrete digital numbers. It is often abbreviated as an ADC, A-to-D, or A/D. ADCs are ubiquitous in all electronic systems. A digital-to-analog converter performs the inverse function and is correspondingly abbreviated as a DAC, D-to-A, or D/A. Figure 15.1 shows the input-output curve of an ADC. The input and output are equal to each other within a quantization error of ± Δ/2, a consequence of the fact that we need to round up or round down real numbers to the nearest integer to represent them digitally. The digital numbers are usually represented with binary digits or bits. If, because of the input statistics, any error between [-Δ/2, + Δ/2] is equally likely, then, from evaluation of the second moment of a flat probability distribution, the rms error of the quantized representation of a real number can be shown to be Δ2/12. If the ADC samples its input at a sampling frequency fS, the power spectrum of the quantization noise is well approximated as being white from 0 to fS/2 and therefore having a noise per unit bandwidth of Δ2/(12(fS/2)).