GATE CS 2024 Set 2 Q28 — Fragmentation and IP Addressing, IPv4, CIDR

To find the CIDR prefix that exactly represents the range of IP addresses from $10.12.2.0$ to $10.12.3.255$, we can analyze the binary representation of the addresses.

Step 1: Calculate the total number of addresses

• The range spans from $10.12.2.0$ to $10.12.3.255$.
• This includes all addresses in $10.12.2.x$ ($256$ addresses) and all addresses in $10.12.3.x$ ($256$ addresses).
• Total addresses = $256 + 256 = 512 = 2^9$ addresses.

Step 2: Determine the prefix length

Since the total number of addresses is $2^9$, the number of host bits is $9$.

Step 3: Find the network address

Let's write the first address of the block, $10.12.2.0$, focusing on the third octet in binary:

• $10 = 00001010_2$ (8 bits)
• $12 = 00001100_2$ (8 bits)
• $2 = \mathbf{0000001}0_2$ (First 7 bits are part of the prefix)

Combining the first $16$ bits of the first two octets and the first $7$ bits of the third octet gives a prefix length of $23$ bits. The remaining $9$ bits (the last bit of the third octet and all $8$ bits of the fourth octet) are set to $0$ for the network address:

Evaluating the Options:

• Option A ($10.12.2.0/23$): Correct. It represents exactly the range $10.12.2.0$ to $10.12.3.255$.
• Option B ($10.12.2.0/24$): Represents only $10.12.2.0$ to $10.12.2.255$ ($256$ addresses).
• Option C ($10.12.0.0/22$): Represents the range $10.12.0.0$ to $10.12.3.255$ ($1024$ addresses).
• Option D ($10.12.2.0/22$): Invalid CIDR notation because the host portion is not all zeros for a $/22$ prefix.