number representation system vs numeration system

number representation system and numeration system both are nouns.

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

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

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

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

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