Appendix A

Binary encoding of quantization levels

Consider an n-bit binary number representing a full-scale range R. In other words, the range R is being quantized into 2n quantization levels. If R is unipolar, the quantized value xQ lies in the range [0,R]. If it is bipolar, xQ lies in the range [−R/2,R/2].

We shall denote the n-bit pattern as a vector b = [bn-1, bn-2, …, b1, b0] where bn-1 is called the most significant bit (MSB) and b0 is the least significant bit (LSB). There are many ways in which this n-bit pattern can be used to encode xQ. Three most common ways are:

• Unipolar natural binary

image

• Bipolar offset binary

• Bipolar two’s ...

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