GATE CS 2005 Q27 — Fragmentation and IP Addressing, IPv4, CIDR

To determine the subnet mask, we analyze the requirements step-by-step:

1. Identify the Class: The organization has a Class B network.
   • Default Class B mask: 255.255.0.0
   • Network bits = $16$, Host bits = $16$.
2. Determine Subnet Bits: We need to create at least $64$ subnets for the departments. Let $k$ be the number of bits borrowed from the host portion for subnetting: $$2^k \ge 64 \implies k = 6 \text{ bits}$$
3. Construct the Subnet Mask: We borrow $6$ bits from the third octet (the first octet of the host portion):
   • First octet: $11111111_2 = 255$
   • Second octet: $11111111_2 = 255$
   • Third octet (borrowing $6$ bits): $11111100_2 = 128 + 64 + 32 + 16 + 8 + 4 = 252$
   • Fourth octet: $00000000_2 = 0$

Combining these, the subnet mask is $255.255.252.0$.