What is the range of possible IP addresses when expressed as decimal and hexadecimal?

Question

I know that there are $2^{32}$ different combinations of IPv4 addresses possible , if expressed in binary.

In decimal notation, they range from $0.0.0.0$ to $255.255.255.255$.

So are there $256^{4}$ possibilities if expressed in decimal?

And $16^{4}$ in hexadecimal?

Thank you.

Answer 1

The number of possible addresses is unaffected by the base you are using to write the addresses. The base is irrelevant to the problem of counting how many possible addresses there are.

Note that the $256^4$ figure you obtained is equal to $2^{32}$. In hexadecimal, the addresses range from $00.00.00.00$ to $\text{FF}.\text{FF}.\text{FF}.\text{FF}$, which gives $16^8 = 2^{32}$ possible addresses. To reiterate: the base only determines how you write the addresses, not the numerical values the address has. There are always $2^{32}$ distinct addresses.