number representation system vs system of numeration

number representation system and system of numeration both are nouns.

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

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

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

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

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