How does fuel gauge on Gen 2 work?

I wonder if someone has technical knowledge about how exactly does the fuel gauge work in Gen 2 Prius? We all know that the fuel gauge can be erratic sometimes and not consistent, but I would like to know how it actually works. Is there a sending unit in the tank that determines the approximate level? I imagine with a bladder that would not work out very well, so how does or North American bladder tank car determine how much fuel is in the tank to display those pips?

The particular reason I am asking is this. My last fill up I had problems filling the tank. Usually those problems do not show up during summer when the bladder is pliable. In any case, last fill-up I had driven over 450 miles on the tank and was pretty sure I was down to fumes, although the last pip was not yet blinking. I knew my wife would be driving a good distance next day and decided to fill up before the pip blinking. I got about 2 gallons in and the pump stopped. I re-adjusted and got 2-3 more gallons in before the pump kicked out again. I knew I was close to empty before the fill-up, so I persisted and re-adjusted the nozzle again and tried again. This time it kicked out almost immediately. I only had less than gallons pumped at that point and I was not giving up. I re-adjusted again and this time the thing went all the way to... (gasp) 11 gallons total. I never pumped that much in one fill-up. low 10's is my max, but usually less than 10. But here is where I got REALLY surprised. As I pulled the nozzle out the gas started to gush out of the tank! that was new to me. Not a lot came out, just a few burps, and I was able to cap the tank and go on my merry way. Now I have almost 300 miles on this tank and the gas gauge is showing 9 out 10 pips. I am a bit worried that something went bad in the system and this is why I would like to know exactly how the system decides how many pips to display.

If anyone knows, please enlighten me. I am a bit worried, but I think it will right itself out eventually. I just can not trust the pips on the gauge at the moment. I think I should be down 5-6 gallons from full. And given I was able to pump 11 gallons last time I should have about 5-6 gallons left and the gauge should be displaying 5 pips, maybe 6, maybe 4, but not 9!

Thoughts?

 

If there is a float type sending unit, how can possibly work well in a bladder that's designed to always have a "full" level? I've been racking my brain on it for a while now. Also, this was the first time that this burping situation happened. Usually I just fill up and it stops the pump at something reasonable, if not always consistent. In the summer I have not had a problem before at all. Always takes a good amount of gas like 9-10 gallons. In the winter I contend with effectively a 9 gallon tank and usually I get about 8+ in it in the winter. But in the warm weather it's been fine. It was possible the pump was being silly, but I was using the pump I usually use at the gas station I usually use. It was not a new to me pump. This is why I wanted to know the technical details of how the fuel gauge worked. If it's a float, how can it determine the proper level if the bladder is constantly squeezing the air out and therefore making the level max? This is the whole purpose for the bladder, isn't it?