Why is IPv4 address space 2^32?

I understand that there are 32 bits in an IPv4 address, with 8 bit octets, but why is the total number of addresses equal to 2^32? I may be over-thinking this, but why is it 2^32 instead of 3^32 or 4, etc. I'm sure I'm looking right past the big picture, so take it easy on me,

Thanks

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Priston

To understand why it's 2^32 you first need to know what a bit is, do you know what a bit is?

Knowing what binary is will also help answer the question.

Heero

How many possible values are in a bit? 2. How many bits are there in an IPv4 address? 32.

2^32

ccnxjr

This actually borders a bit of statistics believe it or not.
Because the actual ip address is a 32 bit number there are exactly 2^32 combinations of 1's and 0's.

So, with binary digits you can only represent a number with a "1" and "0" (2 possible values) .
We've allocated 32 bits for the IP address (or spaces to be populated with a binary digit) .
The question then becomes, how many 32 digit numbers can be formed with the digits "1" and "0"
PR(2, 32) = n^k
(you can look up permutations with repetition)

Interesting question, i'd be surprised to see how many people just repeat what's fed to them from the text book .
(granted, my own answer is from a textbook, it's a different textbook.... ughh... forget it... )

pevangel

It's in the name: binary or base-2.

goldenlight

Can't explain it but this is why.. 00010101.01010101.01010000.01000000

TerminalB

Great stuff guys, makes perfect sense now. Thanks!