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what are /30 /29....?

i) what are those things in red?

ii) how do he know it has 4 IP address, 8 IP address..... are those a standard which cant be modified? or can be calculated when ip changes?

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They are called CIDR, just a short handed form of identifying the Subnet Mask. 

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As @Skiiwee29 said, they are a shorthand form of the subnet mask. It gets tiresome to write 255.255.255.0 all the time. So instead, you write /24 instead. Why 24?

 

Your subnet mask is basically a bit-mask. If you were to write 255.255.255.0 in binary, it would be 11111111.11111111.11111111.00000000, that is a total of 24 1s (so /24). While 255.255.255.252 would be 11111111.11111111.11111111.11111100 or 30 1s (so /30).

 

This is also a hint why /30 results in 4 possible IP addresses: Every bit of your IP address that matches with a "1" in the subnet mask is fixed. Every bit that matches a "0" can be modified. Which means with a subnet mask of /30 you have a total of two bits you can modify. Two bits have four possible values: 00, 01, 10, 11.

 

Another example:

 

Octet-form:

192.168.1.1

255.255.255.0

 

Binary-form:

11000000.10101000.00000001.00000001

11111111.11111111.11111111.00000000

 

The subnet mask tells you that the first three octets can't be modified, while the last octet is variable. Your last octet has 8 bits so 2^8 possible values (=255). So your network has a total of 255 possible IP addresses.

 

Any IP address that does not match the bits of the "fixed part" of your IP address belongs to a different network. So e.g. 192.168.1.25 would be part of your network while 192.168.2.1 would not.

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