To reiterate, this equation can be used to calculate the SNR between an unit amplitude sinusoid and
the quantization error that is made when we quantize the sinusoid with a quantization step size of q. In
the discussion above, we used a step size of 0.1 - this was only for easy presentation of the principles.
Computers do not represent numbers using decimal digits, instead they use binary digits - better known
as bits. With b bits, we can represent 2b distinct numbers. Because we want those numbers to represent
the range between −1 and 1, we could represent 2b−1 quantization levels below zero and 2b−1 above zero
- however, we have not yet represented the zero level itself. To do so, we ’steal’ one binary pattern from
the positive range - now we can only represent 2b−1 − 1 strictly positive levels. The step size is given by