It's pronounced 'b-it' like 'dig-it', not 'bye-t' like 'bye-nary'. Going by linguistics the 'i' must come from 'digit', and a 'bit' is therefore most plausibly

It's pronounced 'b-it' like 'dig-it', not 'bye-t' like 'bye-nary'. Going by linguistics the 'i' must come from 'digit', and a 'bit' is therefore most plausibly a 'b'inary dig'it'. A 'ter'nary dig'it' would be a 'terit', which elides to 'trit'. That sounds like a natural construction, probably why it came about in the first place. You can't drop the 'r' willy nilly because the proto-Indo-European root etymon is 'tr-' not 't-', same in most descendant languages, and 'ter-' is one unexplained corruption of 'tr-' somewhere in the Latin line.