system of numeration vs number representation system

system of numeration and number representation system both are nouns.

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

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

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

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

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