GATE CS 2015 Set 2 Q52 — Fragmentation and IP Addressing, IPv4, CIDR

To find the total number of IP fragments and the offset of the last fragment, we can break down the calculation into the following steps:

1. Calculate the Total IP Payload

The IP packet encapsulates the entire UDP datagram (UDP header + UDP user data):

• $\text{UDP User Data} = 8880 \text{ bytes}$
• $\text{UDP Header} = 8 \text{ bytes}$
• $\text{Total IP Payload} = 8880 + 8 = 8888 \text{ bytes}$

2. Determine Maximum Payload per IP Fragment

The Maximum Transmission Unit (MTU) of the Ethernet LAN is $1500 \text{ bytes}$. Each fragment must include its own IP header ($20 \text{ bytes}$):

$$\text{Maximum Payload per Fragment} = \text{MTU} - \text{IP Header} = 1500 - 20 = 1480 \text{ bytes}$$

Since the fragment offset field in the IP header is measured in units of $8 \text{ bytes}$, the payload size of all fragments (except the last one) must be a multiple of $8$.

Checking if $1480$ is divisible by $8$:

$$\frac{1480}{8} = 185 \quad (\text{which is an integer})$$

Thus, the maximum payload size per fragment is indeed $1480 \text{ bytes}$.

3. Calculate the Number of Fragments

We divide the total IP payload by the maximum payload size per fragment:

$$\text{Number of fragments} = \left\lceil \frac{8888}{1480} \right\rceil = \lceil 6.0054 \rceil = 7$$

The distribution of payload across the $7$ fragments is as follows:

• Fragments 1 to 6: Each carries $1480 \text{ bytes}$ of payload.
• Fragment 7 (Last): Carries the remaining payload: $8888 - (6 \times 1480) = 8 \text{ bytes}$.

4. Calculate the Offset of the Last Fragment

The fragment offset represents the number of payload bytes sent before the current fragment, divided by $8$:

• Payload bytes sent before the $7^{\text{th}}$ fragment $= 6 \times 1480 = 8880 \text{ bytes}$
• Offset of the $7^{\text{th}}$ fragment $= \frac{8880}{8} = 1110$

Therefore, the total number of fragments is $7$ and the offset of the last fragment is $1110$.