GATE CS 2020 Q38 — Fragmentation and IP Addressing, IPv4, CIDR

To find the potential candidate address spaces, we must satisfy three conditions: host capacity, ISP range constraint, and proper CIDR block alignment.

1. Host Capacity: The organization requires $1500$ IP addresses. The smallest power of $2$ that can accommodate this is $2^{11} = 2048$. This requires $11$ host bits, leaving $32 - 11 = 21$ bits for the network prefix. Thus, a $/21$ subnet mask is required. All given options satisfy this.
2. ISP Range Constraint: The ISP's available block is $202.61.0.0/17$. For a $/17$ mask, the first $17$ bits are fixed. The $3^{\text{rd}}$ octet has its most significant bit fixed to $0$ (since $0 = 00000000_2$). Therefore, the $3^{\text{rd}}$ octet can range from $0$ to $127$ ($01111111_2$).
   • Option IV ($202.61.144.0/21$) has a $3^{\text{rd}}$ octet of $144 > 127$, which falls outside the ISP's range.
3. CIDR Block Alignment: For any valid $/21$ block, the $3^{\text{rd}}$ octet must be a multiple of $2^{24-21} = 2^3 = 8$.
   • I. $202.61.84.0/21$: $84$ is not a multiple of $8$. (Invalid CIDR block)
   • II. $202.61.104.0/21$: $104$ is a multiple of $8$ ($13 \times 8$). (Valid)
   • III. $202.61.64.0/21$: $64$ is a multiple of $8$ ($8 \times 8$). (Valid)

Thus, only II and III are potential candidates.