GATE CS 2026 Set 2 Q.33: IPv4/IPv6 Addressing, Subnetting, CIDR, ARP, ICMP and NAT

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 __________. (answer in integer)

Your answer

Official answer and solution

Official answer: 4094
From: Official GATE 2026 answer key

Solution

Count the number of host bits (0s) in the 32-bit subnet mask 255.255.240.0 and compute $2^h - 2$ .

Writing the subnet mask 255.255.240.0 in binary:

First two octets: $8 + 8 = 16$ ones.
Third octet: $240 = 11110000_2$ , which has $4$ ones and $4$ zeros.
Fourth octet: $0 = 00000000_2$ , which has $8$ zeros.

Thus, there are $h = 4 + 8 = 12$ host bits. Excluding the network address (all host bits $0$ ) and the directed broadcast address (all host bits $1$ ), the maximum number of assignable host IP addresses is:

2^{12} - 2 = 4096 - 2 = 4094

Final answer

4094

Common trap

Forgetting to subtract 2 for the network and broadcast addresses.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 2 (CS2)
Question: 33 of 65
Section: Computer Science and Information Technology

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.

Question

Solution

Source