### CS455 - Intro to Computer Networks Homework 2

• Question 1 (20 pts)

• A channel has a total bandwidth of 1 Gbps is shared using the synchronous time division technique

• A period is divided into 640 time slots.

• Question:

• What is the smallest unit of bandwidth reservation that you can make on this system ? (10 pts)

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• A user wants to reserve 50 Mbps transmission capacity on this channel

How many time slots must we reserve to provide this amount of bandwidth reservation ? (10 pts)

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• Question 2 (20 pts)

• A sender node uses a 2 dimensional parity scheme to transmit the following 4 ASCII characters:

 ``` 1010000 0100101 0100010 1001001 ```

The sender uses even parity in rows and in columns and transmits the bits in a row-wise fashion (including the parity bit in each row).

• Show the series of bits transmitted by the sender node. (5 pts)

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In other words: first, encode the above message, then show the transmitted bits.

• A receiving data link layer uses the 2 dimensional parity scheme with even parity for both columns and rows.

 ``` 11110000 01010101 10101010 00001111 ```

As you can see, all rows and columns have even parity. So the receiver will accept this message without errors.

Suppose the messages above that was received in error

Questions:

• Is it possible that the received message has 2 bits that were received in error that the receiver cannot detect ? (5 pts)

• Circle:   Yes     or    No

• If you have circled yes, then show an error pattern with 2 bit errors by circling the bits that are received in error (and is undetectable by the 2-dim parity method):

 ``` 11110000 01010101 10101010 00001111 ```

• Is it possible that the received message has 3 bits that were received in error that the receiver cannot detect ? (5 pts)

• Circle:   Yes     or    No

• If you have circled yes, then show an error pattern with 2 bit errors by circling the bits that are received in error (and is undetectable by the 2-dim parity method):

 ``` 11110000 01010101 10101010 00001111 ```

• Is it possible that the received message has 4 bits that were received in error that the receiver cannot detect ? (5 pts)

• Circle:   Yes     or    No

• If you have circled yes, then show an error pattern with 2 bit errors by circling the bits that are received in error (and is undetectable by the 2-dim parity method):

 ``` 11110000 01010101 10101010 00001111 ```

• Question 3 (10 pts)

• A sender transmits the following bit pattern using the Hammings code:

 ``` 1111111 Bit position: 6543210987654321 ---------------- Bit pattern: 0100000010000001 ```

I put the pattern under a lot of numbers to show the bit positions. You should read the numbers above the bit pattern as:

```      bit position 1, 2, 3, 4, 5, 6, 7,8, 9, 10 , 11, 12, 13, 14, 15, 16
```
from right to left. (The bit positions are written as 16, 15, 14, ..., 4,3,2,1 from left to right.)

• Show the bit pattern that will be transmitted:

 ``` 22222222221111111111 Bit position: 98765432109876543210987654321 ----------------------------- Answer: (line up bit position !) ```

I.e.: encode the above message.

NOTE: You must line up your answer with the bit position as I have done above to receive credit !

• Question 4 (20 pts)

• Note:

 This question is not related to quesrion 3 above !

• A receiver received the following bit pattern that is encoded using Hamming code:

 ``` Bit position: 6543210987654321 ---------------- 0100000010000001 ```

Questions:

• Which one bit will the receiver assume to be in error ? (5 pts)

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• What was the original data that was transmitted ? (5 pts)

 ``` Bit position: 6543210987654321 ---------------- Answer: ```

Further clarification:

 I am asking what is the original data before the Hamming code was applied. You must use the corrected Hamming code word to answer this (the corrected Hamming code word is obtained from the previous question: Which one bit will the receiver assume to be in error ? - correct that bit and use the corrected Hamming code to obtain the original data).

NOTE: You MUST number your answer with the bit position as I have done above to receive credit !

• Show a Hamming code word in which two bit errors were made in the transmission that results in the following bit pattern: (10 pts)

 ``` Bit position: 6543210987654321 ---------------- 0100000010000001 ```

Circle in the above figure the 2 bits that are in error.

Further clarification:

• You must find an Hamming code word yyyyyyyyyyyyyyyy such that:

 ``` Original Hamming code word: yyyyyyyyyyyyyyyy After two bit errors: x x <--- You MUST indicate WHICH | | 2 bits are in error. V V Received by receiver: 0100000010000001 ```

The difficulty of this question lies in the fact that a Hamming code word must pass the Hamming code test (see: click here ).

• Question 5 (20 pts)

• A sender wants to send the following message protected by the CRC polynomial 101:

 ``` 10000001 ```

What is the bit pattern that the sender will transmit ? (10 pts)

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• A receiver using the CRC polynomial 101 receives the following bit pattern:

 ``` 10000001 ```

Will the receiver decide that the message was correct or in error ? Explain to get full credit. (10 pts)

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• Question 6 (10 pts)

• Show the shift-register circuit used to compute the CRC code using the CRC polynomial 1100101 (10 pts)

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