GATE CS 2019 Q28 — Fragmentation and IP Addressing, IPv4, CIDR

To determine which machines belong to the same subnet, we perform a bitwise AND operation between each machine's IP address and the subnet mask, or simply analyze the block sizes determined by the mask.

1. Analyze the Subnet Mask

The subnet mask is given as 255.255.255.252.

• The first three octets (255.255.255) are identical for all three machines, so we only need to examine the last octet.
• The last octet of the mask is $252$, which in binary is $11111100_2$.
• The number of host bits in the last octet is $8 - 6 = 2$ bits.
• This gives a block size (subnet size) of $2^2 = 4$ IP addresses per subnet.

2. Determine the Subnet Ranges

Since the block size is $4$, the subnets for the last octet start at multiples of $4$:

• Subnet 1: $.0$ to $.3$ (Network ID: 100.10.5.0, Broadcast: 100.10.5.3)
• Subnet 2: $.4$ to $.7$ (Network ID: 100.10.5.4, Broadcast: 100.10.5.7)
• Subnet 3: $.8$ to $.11$ (Network ID: 100.10.5.8, Broadcast: 100.10.5.11)

3. Map the Machines to Subnets

• Machine M: IP 100.10.5.2 (Last octet is $2$). It falls in the range $[0, 3]$, so its subnet ID is 100.10.5.0.
• Machine N: IP 100.10.5.5 (Last octet is $5$). It falls in the range $[4, 7]$, so its subnet ID is 100.10.5.4.
• Machine P: IP 100.10.5.6 (Last octet is $6$). It falls in the range $[4, 7]$, so its subnet ID is 100.10.5.4.

Thus, only N and P belong to the same subnet (100.10.5.4/30).