Question

If an IP network uses a subnet mask of \(255.255.240.0\), the maximum number of IP addresses that can be assigned to network interfaces is ______.

Hint:

Count the number of 1 bits in the subnet mask to get the network bits, then use 2 raised to the number of host bits, minus 2 for the network and broadcast addresses.

Answer 1

Correct Answer: 4094

Step 1: Convert the subnet mask to binary.
The subnet mask is \(255.255.240.0\). Writing each octet in binary:
\[ 255 = 11111111,\quad 255 = 11111111,\quad 240 = 11110000,\quad 0 = 00000000 \]

Step 2: Count the number of network bits.
The number of 1s in the mask gives the number of network (prefix) bits. Counting the 1s across all four octets:
\[ 8 + 8 + 4 + 0 = 20 \]
So this is a \(/20\) network.

Step 3: Find the number of host bits.
An IPv4 address has 32 bits in total, so the remaining bits are used to identify hosts within the network:
\[ 32 - 20 = 12 \]
There are 12 host bits.

Step 4: Find the total number of addresses in the network.
With 12 host bits, the total number of distinct addresses is
\[ 2^{12} = 4096 \]

Step 5: Remove the two addresses that cannot be assigned to an interface.
Out of these 4096 addresses, the address with all host bits 0 is the network address, and the address with all host bits 1 is the broadcast address. Neither of these can be assigned to a network interface, so they must be removed:
\[ 4096 - 2 = 4094 \]

Step 6: Final answer.
The maximum number of IP addresses that can be assigned to network interfaces is
\[ \boxed{4094} \]