quantizer has real-valued inputs and integer-valued outputs.

When the quantization step size (?) is small relative to the variation in the signal being quantized, it is relatively simple to show that the mean squared error produced by such a rounding operation will be approximately . Mean squared error is also called the quantization noise power. Adding one bit to the quantizer halves the value of ?, which reduces the noise power by the factor . In terms of decibels,