A binary digit is a bit.
Is there an equivalent term for a three-state digit?
(e.g., a digit representing true, false, or unknown)
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At least, according to Wikipedia:
Analogous to a bit, a ternary digit is a trit (trinary digit)
I think that the question contains a faulty premise. There are many types of three-valued logic. Some three-valued systems include:
I would therefore say that a "digit" representing true, false, unknown is not a digit at all, but rather a nullable boolean, or possibly a tri-state value.
Analogous to a bit, a ternary digit is a trit (trinary digit). One trit contains log23 (about 1.58496) bits of information.
Trits and base 3 computing and hardware have been researched and developed in the 50's. The idea was to eliminate the 2 stage binary comparison by implementing the ternary logic less, equal, or greater outcomes or true, false, or unknown.
I was not able to find any published work with the definition of a trit, but a few articles talking about it and its implementation.
This is the closest to a definition given in American Scientist in an article about the third base:
Setun operated on numbers composed of 18 ternary digits, or trits, ...