number system vs number representation system

number system and number representation system both are nouns.

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

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

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

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

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