that's right.
and yet, I was wrong and it happens that FADECs and EIUs are supplied by DC current. one channel of eng 1 FADEC and EIU 1 are supplied by DC BAT current, and one FADEC and EIU2 by the DC ESS. Both buses are supplied by batteries on ground with the BAT pushbuttons in AUTO.
Oh wait! but ignition is AC. There is no AC on ground, unless they do a pushback at more than 50 kt