GATE CS 2008 Q57 — Fragmentation and IP Addressing, IPv4, CIDR

To find the maximum number of hosts per subnet, we need to determine the number of host bits available in the given subnet mask.

Step 1: Analyze the Subnet Mask
The given subnet mask is 255.255.248.0. Let's convert this mask into its binary representation: $$255.255.248.0 = 11111111.11111111.11111000.00000000$$

Step 2: Count the Host Bits
The host bits are represented by the trailing 0s in the subnet mask:

• Third octet (248): $11111000_2$ contains $3$ zeros.
• Fourth octet (0): $00000000_2$ contains $8$ zeros.

Step 3: Calculate the Maximum Number of Hosts per Subnet
For $h$ host bits, the total number of usable host addresses is $2^h - 2$ (subtracting $2$ for the network address and the directed broadcast address): $$\text{Maximum hosts per subnet} = 2^{11} - 2 = 2048 - 2 = 2046$$

Therefore, the correct option is C.