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Base 2
The binary system.
The base of our number system is 10. However there are mathematical methods of converting bases to 2 , 5 ...e.t.c.
The binary system is the name given to the base-2 number system.
If you mean a number system analogous (similar) to our decimal system, the base for such a number system can be any integer, 2 or greater. In other words, the base can be 2, 3, 4, 5, etc. You need as many different digits as the size of the base (decimal is in base 10, so you need 10 different digits).