Aregister in a computer has a of bits. how many unique combinations can be stored in the register?

The number of unique combinations stored in the register totally dependent upon the number of bits the register can hold.

Explanation:

Suppose if the register is 2-bit.Then it can have (2²) 4 unique combinations of the bits and those combinations are 00,01,10,11.For a 3 bit register there are (2³) or 8 unique combinations those are 000,001,010,011,100,101,110,111.So for a n-bit register there can be 2ⁿ unique combinations there.

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that without the operating systems you would have to control and synchronize computer hardware.