  We present a necessary and sufficient condition to falsify whether a Hawking
radiation spectrum indicates unitary emission process or not from the
perspective of information theory. With this condition, we show the precise
values of Bekenstein-Hawking entropies for Schwarzschild black holes and
Reissner-Nordstr\"om black holes can be calculated by counting the microstates
of their Hawking radiations. In particular, for the extremal
Reissner-Nordstr\"om black hole, its number of microstate and the corresponding
entropy we obtain are found to be consistent with the string theory results.
Our finding helps to refute the dispute about the Bekenstein-Hawking entropy of
extremal black holes in the semiclassical limit.
