2 Network Ranges and Usable Hosts

How prefixes divide IPv4 addresses

An IPv4 address contains $32$ bits. In CIDR notation, an address is followed by a prefix length, as in 192.168.10.77/26. The prefix length $p$ identifies the leading network bits; the remaining $32-p$ bits are host bits and identify addresses within that network. This is equivalent to a subnet mask with $p$ leading $1$ bits.

Calculating network and broadcast addresses

For a prefix length $p$, set all host bits to $0$ to find the network address, and set all host bits to $1$ to find the broadcast address. The total number of addresses in the block is

For conventional subnets from /0 through /30, the usable host count is the total address count minus two, because the network and broadcast addresses are reserved.

Finding a subnet with the block size

To work in decimal, find the octet where the mask stops being 255 or becomes less than 255. The block size in that octet is $256 - \text{mask value}$. The network starts at the multiple of that size that contains the given address, and the broadcast address is the end of that block.

Example: 192.168.10.77/26

A /26 mask is 255.255.255.192. The last-octet block size is $256 - 192 = 64$, so the subnet blocks begin at 0, 64, 128, and 192. Since the last octet 77 falls in the block from 64 through 127, the results are:

• Network: 192.168.10.64

• Broadcast: 192.168.10.127

• Usable host range: 192.168.10.65–192.168.10.126

• Total addresses: $2^6 = 64$

• Usable hosts: $64 - 2 = 62$

The input address 192.168.10.77 is a usable host address in this subnet, not the network or broadcast address.

Prefix length and host capacity

The number of host bits is $32-p$. For ordinary subnets, the prefix length determines the host capacity:

• /24 has $8$ host bits, $256$ total addresses, and $254$ usable hosts.

• /26 has $6$ host bits, $64$ total addresses, and $62$ usable hosts.

• /30 has $2$ host bits, $4$ total addresses, and $2$ usable hosts.

A larger prefix length leaves fewer host bits and creates a smaller address block. For example, /26 contains fewer addresses than /24.

Special cases for /31 and /32

The usual rule of subtracting two addresses has exceptions.

• A /31 contains two addresses and is used on point-to-point links. Both addresses can be assigned to the link endpoints; neither is treated as the conventional network or directed-broadcast address.

• A /32 contains one address and represents a single-address prefix, often used as a host route.

Checking a subnet calculation

Use these checks to verify a subnet calculation:

1. Confirm that the prefix is between /0 and /32.

2. Check that the network address has all host bits set to $0$ and the broadcast address has all host bits set to $1$.

3. Verify that the given IP address falls between the calculated network and broadcast addresses.

4. For ordinary subnets, confirm that the usable range excludes those two endpoints. Apply the /31 and /32 exceptions where relevant.

• point-to-point link