“I was just north of Dundee when I checked my fuel gauges and it said it was half full, but when I checked the wing gauges, one said it was empty and the other said I had only half an hour left of flying.”
The electronic fuel guage on the FDCT is set by the pilot prior to flight on the basis of the physical quantity of fuel in the tanks, established by dipping. The electronics will then calculate fuel remaining on the basis of fuel burn.
If the electronic guage is set incorrectly to start with then it is quite possible that the it could show more fuel available then there actually is - hence the reason sight guages are available in the cockpit.