The most basic computing task that a computer does is to operate a single logic gate. Whether that gate is implemented with a vacuum tube, a transistor, or a few layers of molecules inside a chip, it’s the fundamental operation that all calculations are based upon. Even bit-shifting and such involves more than one logic gate.
The most basic task a computer can do is act as a paperweight or a doorstop or the like. The computer doesn’t even need to be turned on to do that.