half a dozen vs digit

half a dozen and digit both are nouns.

Word	Noun	Adjective	Verb	Adverb
half a dozen	Yes	No	No	No
digit	Yes	No	No	No

As nouns, digit is a hypernym of half a dozen; that is, digit is a word with a broader meaning than half a dozen:

Other hypernyms of half a dozen include figure.

half a dozen (noun)	digit (noun)
the cardinal number that is the sum of five and one	a finger or toe in human beings or corresponding body part in other vertebrates
	one of the elements that collectively form a system of numeration
	the length of breadth of a finger used as a linear measure