just musing here from an old hardware guy
...\start daydream with boring anecdote
i once encountered in a TTL system a 3 level logic circuit that used "High" and "Low" TTL voltage levels but also detected and acted on a third level "In Between" ,
its purpose was to detect multiple slave responses to an address query from master.
Address_Acknowledge line driven high meant no response yet, middle meant single response (good) , low meant multiple responses(failure, program should try again)
That astonished me because i had never heard of anything but base two Boolean " High Low " for logic circuits.
I asked my old mentor and he said said "Sure, you can do math with any radix you want and it doesn't even have to be an integer. Mathematically it can be shown that a base e machine will require the least number of gates but i don't know of anybody who's developed a base e arithmetic book. "
Base e arithmetic? I can't even count in base e.
I soon figured out "well sure, i guess one could use any number of voltage levels for his logic,
and analog computing is just the limit as that number approaches infinity."
I bought a book on irrational numbers planning to learn how to count in an irrational number base maybe √2 but it was way too abstract for my flea brain.
That was almost forty years ago. Now i find lots of links on ternary (base 3) computing and even a few on base e. Try a search if you're curious .
As i said analog implies an infinite number of levels/values. There's a major practical drawback to analog circuits you have to keep them calibrated so that everybody attached to a particular signal agrees on its value . Some smaller number of logic levels might be easier to build and keep working..
Point being , i laud your investigating alternatives to binary computing and suggest there might be diminishing returns beyond some number of levels .
"e" being closer to 3 than 2 the point of diminishing returns might be around there . I find it a fascinating concept.
Seems to me you could build a cell out of something like a dollar Pic microcontroller
http://www.digikey.com/product-search/en/integrated-circuits-ics/embedded-microcontrollers/2556109?k=&pkeyword=&v=150&FV=fff40027,fff800cd&mnonly=0&newproducts=0&ColumnSort=0&page=1&quantity=0&ptm=0&fid=0&pageSize=25
controlling a digital potentiometer , a hybrid if you will,
and explore the behavior of multi-level computing machines.
It wouldn't get you to true analog though.\end daydream
sorry if I've bored you
old jim