While sleeping, human brain is also sleeping.
This is not so. The human body rests during sleep while the brain is very much active. During sleep the brain is recharging its batteries and still very much in control of the majority of bodily functions, including breathing. As we sleep we go back and forth between two "sleep states", these being Rapid Eye Movement sleep (abbreviated to REM and the period in which we dream) and Non-Rapid Eye Movement Sleep (or NREM).