CS455 - Introduction to Computer Networks Homework 1

Solutions

• Question 1 (10 pts)

• Show the content that a web browser (such as firefox) will receive when you enter the following URL in the browser:

 ``` http://www.mathcs.emory.edu/~cheung ```

 ``` Type: telnet www.mathcs.emory.edu 80 GET http://www.mathcs.emory.edu/~cheung HTTP/1.0 You will received this message: 301 Moved Permanently

Moved Permanently

The document has moved here.

Apache/2.0.63 (Unix) DAV/2 mod_ssl/2.0.63 OpenSSL/0.9.7d Server at webhome2.mathcs.emory.edu Port 80
```

• Question 2 (10 pts)

• Show in the figure below a sine wave that has the frequency of 1000 Hz (1 msec = 1 milli second = 0.001 sec):

• Show in the figure below a sine wave that has the frequency of 500 Hz:

• Question 3 (10 pts)

• Consider the following input signal:

Show the resulting when the input signal is modulated onto a 2000 Hz sine wave using amplitude modulation:

• Queston 4 (20 pts)

• Suppose you want to improve the quality of transmission of voice over the telephone by transmitting all frequencies between 20 Hz and 8000 Hz over a digital transmission channel

What sampling rate do you need to use to re-construct the voice input reliably ? (10 pts)

 ``` You need to sample at the Nyquist rate: 2 × 8000 = 16,000 Hz ```

Each sample is represented by an integer value between -64 and 63.

What is the data rate of a voice transmission using the above scheme: (10 pts)

 ``` 1 sample is represented by 7 bits (-64 to 63 = 128 values) 16,000 samples per sec will produce: 16,000 × 7 = 112000 bits / sec ```

• Question 5 (20 pts)

• A sender uses NRZ to transmit an (long) serie of bits to a receiver.

The receiver reads the transmission at precisely the middle of its clock to determine the value of the transmitted bit.

The sender's clock runs at 1000 Hz and the receiver's clock runs at 999 Hz.

Suppose the receiver does not re-synchronize its clock to the sender's clock.

If the sender's and the receiver's clocks are synchronized at the start of a (long) transmission, which bit poistion is the first bit that the receiver will receive incorrectly due to the clock drift ?

• Questin 6 (10 pts)

• Show the digital signal using NRZ when you transmit the following data:

 10110010 (3pts)

• Show the digital signal using NRZ when you transmit the following data:

 10110010 (3pts) using 4B/5B (4 pts)

• Show the digital signal using Manchester code when you transmit the following data:

 10110010 (3pts)

• Question 7 (10 pts)

• Transmit the data 1010 using a 2-level amplitude modulation where the 0 bits have half the amplitude of the 1 bits

Use 4 units in the graph below to transmit each bit

Use 2 sine waves for each bit

• Transmit the data 1010 using a 2-level frequency modulation where the 0 bits have half the frequency of the 1 bits

Use 4 units in the graph below to transmit each bit

Use 2 sine waves to transmit a 0 bit and 4 sine waves to transmit a 1 bit

• Transmit the data 1010 using a 2-level phase modulation where the 0 bits have 0 phase shift and the 1 bits have 180 degrees phase shift

Use 4 units in the graph below to transmit each bit

Use 2 sine waves to transmit a each bit

• Question 8 (10 pts)

• Suppose that the bandwdith of optical fiber is 1 GHz

If the the signal to noise ratio is 100, what is the maximum data transmission rate on this optical fiber: (5 pts)

 ``` MAx data rate = Bandwidth × 2log(1 + S/N) = 1,000,000,000 × 2log(1 + 100) = 1,000,000,000 × 6.658 = 6,658,000,000 bits / sec = 6.658 Gbps ```

If the the signal to noise ratio is 1000, what is the maximum data transmission rate on this optical fiber: (5 pts)

 ``` Max data rate = Bandwidth × 2log(1 + S/N) = 1,000,000,000 × 2log(1 + 1000) = 1,000,000,000 × 9.967 = 9,967,000,000 bits / sec = 9.967 Gbps ```