Sleep-deprived rats showed impaired performance while acting fully awake.
During wakefulness, our brain wave patterns are typically fast and of low-amplitude. This is different from the slow, high-amplitude non-REM phases of sleep. Researchers have discovered that, at least in rats, when they were sleep-deprived the rats appeared fully awake, but showed increasing impairment on behavioral tasks. There was also electrical evidence that some neurons were "asleep" and not firing. This evidence supports the idea that sleep-deprived individuals who claim to be fully awake may actually have some of their neurons asleep.
PositiveTip: Get regular, adequate sleep to avoid impaired mental function.