IP Networking

I know IPv4 is a 32 bit address space, and we write it as 4 octets. But does IP interpret the address as 4 octets or full 32 bit value?

Example:
Dotted decimal = 192.168.1.1
4 octet binary = 11000000.10101000.00000001.00000001
full binary = 11000000101010000000000100000001
Full decimal = 3232235777

On my browser, I discovered today that I could type http://3232235777 instead of http://192.168.1.1.

Does IP ever compute with the full binary value? In other words, does IP only look at the 4 octet binary value...

11000000.10101000.00000001.00000001

...or does it ever look at a "full value" without any octet boundaries...

11000000101010000000000100000001

Suppose I have address 192.192.0.192/24, and write out in binary with no octet boundaries...

IP = 11000000110000000000000011000000 decimal = 3233808576
netmask = 11111111111111111111111100000000 decimal = 4294967040
network = 11000000110000001100000000000000 decimal = 3233857536

Do the values 3233808576 and 3233857536 have any meaning? I'm not asking if IP computes in decimal or if the decimal numbers are used in the IP software, I'm asking if the numerical values themselves (without any octet boundaries) have any meaning.

Sometimes the network address is > IP, sometimes the IP > network address.

Such as 192.192.192.192/24
IP = 11000000110000001100000011000000 decimal = 3233857728
network = 11000000110000001100000000000000 decimal = 3233857536
Here, the IP > network.

I'm guessing IP doesn't really operate with the full values, and the only arithmetic it does is with the octets, masks and logical AND, OR, NOT operations.

I wonder with VLSM, this matters. However, IP is a hierarchical system, so the masks and the networks have meaning.

The octets are what the value represents, not a physical "thing". Bits are bits as far as a computer's concerned. No, just the bits they represent. Tell me, what's the difference between

Code:

    0 0 0 0
AND 1 1 1 1
=   0 0 0 0

vs
    0000
AND 1111
=   0000

Logically nothing. No reason to break the bits, or even the octets apart to do simple logical operations like AND/OR/XOR/NOT. It can do everything in one operation. They didn't just happen to use masks instead of some other concept, they wanted something easy to build in hardware. They're designed in such a way that the meanings translate into machine concepts very well. You don't have to care whether a netmask is 32 bits or 4 octets when doing masking and comparison.