The basic task of the A/D converter is to convert a continuous range of input amplitude into a discrete set of digital code words. This conversion involves the processes of Quantization and Coding.

The term Full scale (FS) is used for uni-polar signals.

The term Full-scale range (FSR) is used to describe the range of an A/D converter for bipolar signals (i.e., signals with both positive and negative amplitudes).

The coding process in an A/D converter assigns a unique binary number to each quantization level. If we have L levels, we need at least L different binary numbers. With a word length of b + 1 bits we can represent 2b+1 distinct binary numbers. Hence we should have 2(b+1) > L or, equivalently, b + 1 > log2 L. Then the step size or the resolution of the A/D converter is given by

If a zero is assigned a decision level, the quantizer is of the midrise type.

If a zero is assigned a quantization level, the quantizer is of the mid treat type.

The quantization error eq(n) is always in the range – \\(\\frac{\\Delta}{2}\\) < eq(n) ≤ \\(\\frac{\\Delta}{2}\\), where Δ is quantizer step size.

The possible outputs of the quantizer (i.e., the quantization levels) are denoted as \\(\\hat{x}_1, \\hat{x}_2,…\\hat{x}_L\\). The operation of the quantizer is defined by the relation, xq(n) ≡ Q[x(n)]= \\(\\hat{x}_k\\), if x(n) ∈ Ik.

If the dynamic range of the signal, defined as xmax-xmin, is larger than the range of the quantizer, the samples that exceed the quantizer range are clipped, resulting in a large (greater than \\({\\Delta}{2}\\)) quantization error.

We note that practical A/D converters may have offset error (the first transition may not occur at exactly + 1/2 LSB).