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BC range problem

I'm having a problem with my wife's '88 US E-28 M5.  Seems that the range 
function on the Bord Computer has started thinking that there's a lot more 
fuel in the tank than there actually is.  This means that the range shows 
around 150 miles when the engine sputters to a stop, something my wife isn't 
too terribly keen on.

I'm not sure, but I think that the mileage function is working OK.  MPG 
lately seems higher than I recall at 70 mph (now around 22 vs18 if I recall 
when it was new), but I don't drive the car all that often and it could the 
Dinan chip that wasn't in there before.

When I check the tank sender signal to the unit (press 1000 and 1 
simultaneously to show volume in liters) it indicates around 32 liters with 
the sender out and the float at empty.  The adjustment on the front only 
lets you change it by about +/- six liters, so it's no help.

I've tried tracing down the signal from the instrument cluster to the BC 
unit to see if there's a weak connection, but so far can't find anything 
(the fuel gauge reads correctly).

I'm wondering if the Service Interval batteries aren't dying, but she's not 
getting any of the textbook symptoms.

I'd appreciate hearing what others think could be the problem.