The title of the question is pretty self-explanatory.
I did a quick back-of-the-envelope calculation for my own digital calculator watch (the Casio CA-53W for those who are interested). The battery is supposed to last around 5 years on the 90 mAh coin cell inside. This means that the watch must be using $$0.090\ \mathrm{Ah}\ /\ (5\ \mathrm{years} * 365\mathrm{\frac{days}{year}} * 24\mathrm{\frac{hours}{day}}) = 2.055\times10^{-6} $$ or just over 2 µA!!!
Now, I know that with enough tweaking, the ubiquitous ATMega328p can use as little as 1 µA, and there are specialized microcontrollers out there that use even less, say in the tens of nanoamps...
...but what about the display? My watch shows the time on a 7-segment lcd, and the display is never off. Where on Earth can I find a display that only uses something on the order of 1 or 2 µA??
(Incidentally, I'm just trying to make own simple Reverse Polish calculator watch, kind of like the µwatch project at calcwatch.com, but with a focus on long battery life.)
Would I need to buy an fpga, fuse my own logic circuit onto it, and somehow hack the display out of an old watch to get these kinds of results? Is there an easier way?