number representation system vs number system

number representation system and number system both are nouns.

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

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

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

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

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