Does FADEC still work when the battery runs out? Its electric too.
FADEC systems have their own alternators. The alternators are mechanically driven by the spinning of the engine (down to very low rpms). Even an idling engine is spinning up to 10 times as fast as the speed required for EEC (or ECU) power.
The alternator uses a permanent magnet to generate electricity (actually, each alternator has two power-generating circuits to provide power to independent channels (computers) in the EEC's. There is a normal channel and a backup channel in the EEC).
A great deal of redundancy is built into the engine management system
