numeration system vs number representation system

numeration system and number representation system both are nouns.

Word	Noun	Adjective	Verb	Adverb
numeration system	Yes	No	No	No
number representation system	Yes	No	No	No

As nouns, numeration system and number representation system are synonyms defined as:

numeration system and number representation system: any notation for the representation of numbers

Other synonyms of numeration system include number system, system of numeration.

numeration system (noun)	number representation system (noun)
any notation for the representation of numbers	any notation for the representation of numbers