Two. 0 and 1. Any system uses as many single digits as the nominal base.
Base 10 uses 10: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Base 16 (hexadecimal) uses 16: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e and f.
etc.
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four
7 digits
It would be 2 raised to the power 32: 4,294,967,296.
4 these are 00,01,10 and 11...
There are infinitely many numbers in each system, however base 10 uses 10 digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and binary uses 2 digits {0, 1}. The maximum digit is one less than the base.