If you're interested in research, the International Symposium on Multivalued Logic has been studying this area for 50 years: http://www.mvl.jpn.org/ISMVL2020/
As far as practical applications of non-binary circuitry, the Intel 8087 math co-processor used 4-level circuitry in its ROM. (This chip was used in the IBM PC.) Intel needed to do this to fit the large microcode ROM on the chip. The chip's logic, though, was regular binary. http://www.righto.com/2018/09/two-bits-per-transistor-high-d...
> As far as practical applications of non-binary circuitry, the Intel 8087 math co-processor used 4-level circuitry in its ROM. (This chip was used in the IBM PC.) Intel needed to do this to fit the large microcode ROM on the chip.
Also, as noted at the bottom of that article, most modern flash storage uses multi-level cell technologies that allow two, three, or four bits of data to be stored per memory cell rather than just one. This obviously significantly increases data density and allows for cheaper drives at the cost of reduced write performance, reduced endurance, and more error correction being necessary for reliable operation.
As far as practical applications of non-binary circuitry, the Intel 8087 math co-processor used 4-level circuitry in its ROM. (This chip was used in the IBM PC.) Intel needed to do this to fit the large microcode ROM on the chip. The chip's logic, though, was regular binary. http://www.righto.com/2018/09/two-bits-per-transistor-high-d...