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## IS250 Computer Based Communications Networks and Systems

Spring 2010

Assignment 2 Solutions

Assignment 2 is due at 2pm (before start of class) on Tuesday 2/16. Please see grading policy on course homepage for additional details regarding early/late submissions.

1. In the lecture slides, we discussed how a data string "10110010" is encoded by USB using a NRZ-I scheme.

(a) Show how the same data string is encoded by Ethernet, using the Machester Encoding scheme.

```  +--+--+     +--+  +-----+  +--+     +-----+
```
```  |     |     |  |  |     |  |  |     |     |
```
```  |     |     |  |  |     |  |  |     |     |
```
```--+     +--+--+  +--+     +--+  +-----+     +--
```
```  1     0     1     1     0     0     1     0
```

(b) In what way is the Machester Encoding scheme superior (or not) to the NRZ-I scheme?

Manchester encoding has a built-in synchronization mechanism, since the signal always include a transition for each bit of data transmitted. Therefore, a long sequence of zero bits, which may be problematic to decode in an NRZ-I scheme, can be properly decoded in the Manchester encoding scheme.

2. Channel capacity:

(a) If two signal levels are used, what is the data rate that can be sent over a coaxial cable that has an analog bandwidth of 6.2MHz? (Comer 7.22)

D < 2*B log_2(K)
2*6.2Mhz*log_2(2) = 12.4 Mbps

(b) If a telephone system can be created with a signal-to-noise ratio of 40dB and an analog bandwidth of 3000 Hz, how many bits per second can be transmitted? (Comer 7.25)

40dB = 10^(40/10) = 10000
C = B * log_2(1 + S/N)
C = 3000 Hz * log_2 (1 + 10000)
C = 39864 bits per second

3. Using Shannon's Theorem, explain why practical amplitude modulation systems keep the carrier near maximum strength. (Comer 10.3)

According to Shannon's Theorem, channel capacity is a function of the signal-to-noise ratio of the transmitted signal. The higher the signal strength, the greater the channel capacity. Therefore, keeping the carrier at or near maximum signal strength will provide the highest possible signal-to-noise ratio and channel capacity.

4. What is the difference between modulation and multiplexing?

Modulation refers to the method of altering a carrier wave's amplitude, frequency or phase for the sake of transmitting a single information signal. Multiplexing, on the other hand, refers to sharing a single medium for the sake of transmitting multiple, distinct information streams.

Note: For Question 1(a), you can show the resulting waveform using a fixed-width font (see example below) or attach an image file to your submission.

` --+  +--+  +--   |  |  |  |   |  |  |  |   +--+  +--+ `