  Quantum random number generators (QRNGs) can provide genuine randomness based
on the inherent unpredictable nature of quantum physics. The extracted
randomness relies not only on the physical parts of the QRNG, such as the
entropy source and the measurement device, but also on appropriate
postprocessing method. The m-least significant bits (m-LSBs) operation is one
of the simplest randomness extraction method, which has the advantage of easy
implementations. Nonetheless, a detailed analysis of the m-LSBs operation in
QRNGs is still missing. In this work we give a physical explanation of the
m-LSBs operation by introducing a new positive operator-valued measurement
operator, which is obtained by regrouping the results of coarse-grained
measurements. Both trusted and untrusted source scenarios are discussed. The
results show that the m-LSBs operation can extract randomness effectively under
the condition of the trusted source, while it is not effective under the
untrusted source scenario.
