Subnetting (IP Networks)

What is subnetting?

A subnet mask yields which bits in a network IP are already occupied (called the routing prefix) and which are available (which are the host identifiers).

For instance, consider the mask 255.255.255.0. (in IPv4, i.e. 8 bits per “number” separated by dots) (Prints below are from the CyberMentor’s worksheet for subnetting.)

The number in each subnet mask is the sum of the powers of the active/occupied bits: when all (eight) bits are active, the sum evaluates to 255

$$\sum _{k=0}^7{2}^k=\frac{2^{7+1}-1}{2-1}=255$$

The backslash notation indicates how many bits in total are active/occupied (in the case above, /24 means that 24 bits are active).

The number of total hosts available in a subnet is equal to $2$ to the power of the inactive bits (since each one can either be on/off), although usually the number is actually this total minus 2 (to account for the netmask address as well as the broadcast address).

Example

• The mask is 255.255.255.0: thus, only the last part is mutable, while the others are constant (i.e. all hosts will be of the form 192.168.57.x).
• The netmask address defaults to 192.168.57.0, the first available host
• The broadcast address defaults to 192.168.57.255, the last available host
• The number of free available hosts is, thus, $2^8-2=254$

Rule for calculating subnet masks from unoccupied bits

Notice that

$$255=\sum _{k=0}^7{2}^k=2^{7+1}-1=2^8-2^0$$

is the sum for $8$ occupied bits (i.e. $0$ unoccupied bits).

For $1$ unoccupied bit, the sum goes to $2^8-1-1=2^8-2^1$. For $2$ unoccupied bits, the sum goes to $2^8-1-1-2=2^8-2^2$ etc.

Thus, for $0\le m\le 8$ unoccupied bits, we have the formula for the corresponding subnet mask’s number

$$2^8-2^m$$

Notice that it generalizes even for the case of all ($8$) available bits, for which the respective submask number goes to $0$ (!).

Exercise

Network IP	Subnet	Available Hosts	Network	Broadcast
192.168.0.0/22	255.255.$(2^8-2^{22-16})$.0	$2^{32-22}-2=1024-2$	192.168.0.0	192.168.3.255
192.168.1.0/26	255.255.255.($(2^8-2^{32-26}$)	$2^{32-26}-2=64-2$	192.168.1.0	192.168.1.63
192.168.1.0/27	255.255.255.($(2^8-2^{32-27}$)	$2^{32-27}-2=32-2$	192.168.1.0	192.168.1.31