IN STEP 1 GIVE THE INTRODUCTION OF THE CONCEPT AND GIVE ANSWER FOR EACH PART OF THE QUESTION IN EACH DIFFERENT STEP WITH CLEAR EXPLANATION AND IN THE FINAL STEP GIVE THE WHOLE FINAL ANSWER IN JUST VERY FEW SENTENCES AND MOREOVER I NEED COMPLETE AND CLEAR ANSWER at last explain what we did in each step in just few sentences1. A router performs longest prefix matching on IP destination addresses. To
simplify this exercise, we assume all IP addresses are only 8 bits long (instead of the usual
32 bits in IPv4). This means every IP address is a binary string between 00000000 and
11111111, representing decimal values from 0 to 255. The router uses the following forwarding
table:
10 A
100 B
101 Cc
1 D
(a) (8 points) For each prefix, determine the number of addresses it could potentially match
(without considering longest prefix matching). Express the range in binary and count.
Ezample: the prefix “10” matches all addresses starting with “10”, i.e., from 10000000
to 10111111. Besides if a prefix has n bits, it matches 28" addresses.
(b) (8 points) Now, apply longest prefix matching. For each prefix, how many addresses are
actually routed to its interface?
(c) (4 points) Identify any prefix that is fully redundant — meaning it does not affect
forwarding for any address. Clearly explain why it is redundant.
Question:
IN STEP 1 GIVE THE INTRODUCTION OF THE CONCEPT AND GIVE ANSWER FOR EACH PART OF THE QUESTION IN EACH DIFFERENT STEP WITH CLEAR EXPLANATION AND IN THE FINAL STEP GIVE THE WHOLE FINAL ANSWER IN JUST VERY FEW SENTENCES AND MOREOVER I NEED COMPLETE AND CLEAR ANSWER at last explain what we did in each step in just few sentences1. A router performs longest prefix matching on IP destination addresses. To
simplify this exercise, we assume all IP addresses are only 8 bits long (instead of the usual
32 bits in IPv4). This means every IP address is a binary string between 00000000 and
11111111, representing decimal values from 0 to 255. The router uses the following forwarding
table:
10 A
100 B
101 Cc
1 D
(a) (8 points) For each prefix, determine the number of addresses it could potentially match
(without considering longest prefix matching). Express the range in binary and count.
Ezample: the prefix “10” matches all addresses starting with “10”, i.e., from 10000000
to 10111111. Besides if a prefix has n bits, it matches 28" addresses.
(b) (8 points) Now, apply longest prefix matching. For each prefix, how many addresses are
actually routed to its interface?
(c) (4 points) Identify any prefix that is fully redundant — meaning it does not affect
forwarding for any address. Clearly explain why it is redundant.
This is AI generated Response.
Asked by: Test User 100300
Created at: 2025-05-16 16:09:38
Final Answer:
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**STEP 1: Introduction to the Concept**
This problem deals with **longest prefix matching** in IP routing. Here, every IP address is 8 bits long (from 00000000 to 11111111, i.e., 0 to 255). The router uses prefixes to decide which interface to send a packet to. Without considering longest matching, a prefix matches all addresses starting with its bits. With longest matching, an address goes to the interface with the most specific (longest) matching prefix.
---
**STEP 2: Answer Part (a)**
*For each prefix, determine the number of addresses it could potentially match (without considering longest prefix matching). Express range and count.*
- **Prefix: `10` (2 bits)**
- Matches all addresses starting with `10`.
- Range: `10000000` to `10111111` (binary), which is 128 to 191 (decimal).
- Count: \(2^{8-2} = 2^6 = 64\) addresses.
- **Prefix: `100` (3 bits)**
- Matches all addresses starting with `100`.
- Range: `10000000` to `10011111` (binary), which is 128 to 159.
- Count: \(2^{8-3} = 2^5 = 32\) addresses.
- **Prefix: `101` (3 bits)**
- Matches all addresses starting with `101`.
- Range: `10100000` to `10111111` (binary), which is 160 to 191.
- Count: \(2^{8-3} = 2^5 = 32\) addresses.
- **Prefix: `1` (1 bit)**
- Matches all addresses starting with `1`.
- Range: `10000000` to `11111111` (binary), which is 128 to 255.
- Count: \(2^{8-1} = 2^7 = 128\) addresses.
---
**STEP 3: Answer Part (b)**
*Apply longest prefix matching. For each prefix, how many addresses are actually routed to its interface?*
- **Prefix: `100`**
- More specific than `10` and `1`, so it gets all 32 addresses from 128 to 159.
- **Prefix: `101`**
- More specific than `10` and `1`, so it gets all 32 addresses from 160 to 191.
- **Prefix: `10`**
- Only gets addresses not matched by `100` or `101` in the `10` range.
- But all `10xxxxxx` addresses (128 to 191) are covered by `100` or `101`.
- So, **0** addresses for `10`.
- **Prefix: `1`**
- Only matches addresses starting with `1` not covered by more specific prefixes.
- Addresses from 192 to 255 (`11000000` to `11111111`) are not covered by any more specific prefix.
- So, **64** addresses for `1`.
---
**STEP 4: Answer Part (c)**
*Identify any prefix that is fully redundant—meaning it does not affect forwarding for any address.*
- **Prefix `10` is fully redundant**.
- All addresses it could match (128 to 191) are already matched more specifically by `100` or `101`.
- Thus, it never affects forwarding for any address.
---
**STEP 5: Final Answer (Summary in Few Sentences)**
- Prefix `100` matches 32 addresses, `101` matches 32, `1` matches 64, and `10` matches none due to longest prefix matching. The prefix `10` is fully redundant because all its addresses are already matched by more specific prefixes.
---
**STEP 6: What We Did in Each Step**
1. Introduced the concept of longest prefix matching in IP routing.
2. Calculated the address range and count for each prefix without longest prefix matching.
3. Determined, using longest prefix matching, how many addresses each prefix actually forwards.
4. Identified the redundant prefix and explained why.
5. Summarized the final answer concisely.
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1. A router performs longest prefix matching on IP destination addresses. To
simplify this exercise, we assume all IP addresses are only 8 bits long (instead of the usual
32 bits in IPv4). This means every IP address is a binary string between 00000000 and
11111111, representing decimal values from 0 to 255. The router uses the following forwarding
table:
10 A
100 B
101 Cc
1 D
(a) (8 points) For each prefix, determine the number of addresses it could potentially match
(without considering longest prefix matching). Express the range in binary and count.
Ezample: the prefix “10” matches all addresses starting with “10”, i.e., from 10000000
to 10111111. Besides if a prefix has n bits, it matches 28" addresses.
(b) (8 points) Now, apply longest prefix matching. For each prefix, how many addresses are
actually routed to its interface?
(c) (4 points) Identify any prefix that is fully redundant — meaning it does not affect
forwarding for any address. Clearly explain why it is redundant.