GATE CS 2017 Set 2 Q20 — Fragmentation and IP Addressing, IPv4, CIDR

To find the maximum number of IPv4 router addresses that can be listed in the Record Route (RR) option, we analyze the constraints on the IPv4 header size:

1. Maximum IPv4 Header Size: The Internet Header Length (IHL) field in the IPv4 header is $4$ bits wide. The maximum value it can hold is $15$ (in $32$-bit words). Therefore, the maximum size of an IPv4 header is:$$\text{Max Header Size} = 15 \times 4 \text{ bytes} = 60 \text{ bytes}$$
2. Base Header Size: The minimum (base) IPv4 header size without any options is $20$ bytes.
3. Maximum Space for Options: $$\text{Max Option Space} = 60 \text{ bytes} - 20 \text{ bytes} = 40 \text{ bytes}$$
4. Record Route (RR) Option Overhead: The Record Route option format contains $3$ bytes of control information:
   • Type: $1$ byte
   • Length: $1$ byte
   • Pointer: $1$ byte
   This leaves the remaining space for storing IPv4 addresses:$$\text{Space for IP addresses} = 40 \text{ bytes} - 3 \text{ bytes} = 37 \text{ bytes}$$
5. Number of IPv4 Addresses: Each IPv4 address requires $4$ bytes. $$\text{Maximum number of addresses} = \left\lfloor \frac{37}{4} \right\rfloor = 9$$

Thus, the maximum number of IPv4 router addresses that can be listed is 9.