CS601 Assignment 1
Question No. 1
Suppose we want to send a binary signal through a 6 KHz channel having signal-to-noise ratio is 30 dB.
What will be the maximum achievable data rate? Provide your answer with complete calculations and
proper unit.
Question No. 2
In a university campus, total 6 gateways of several computer LABs are connected with each other using
mesh topology. In each LAB, star topology is used to connect different devices with a central switch.
How many links have been used to connect these gateways with each other? Provide your answer by
mentioning the formula and all necessary calculation steps.
Solution:
Question 1: Solution:
Given:
Bandwidth =B = 6kHz = 6000Hz
SNR in dB = 30dB
To Calculate the maximum achievable data rate of a binary signal through a channel, we can use the
Shannon’s Formula:
C=B log2(1+ SNR)
First to convert the SNR in dB to SNR:
Using Formula:
SNR(dB) = 10log10(SNR)
30=10log10(SNR)
30/10=log10(SNR)
3= log10(SNR)
Taking exponentional on both sides
103= 10log10(SNR)
SNR=103
SNR=1000
Put the values in Shannon’s Formula:
Solve the log2(1001) by applying the change of base formula
Now,
“log10(1001)” which is very close to 1000(which is 103) we can take approximate value which is “3”
Then,
The value of “log10(2)” is approximately 0.301
Putting the both values into change base formula
Now,
Calculate the channel capacity
bits per second Ans
Question 2: Solution:
In a mesh topology, every gateway is connected to every other gateway.If there are n gateways, the
number of links required to connect all gateways can be calculated using the formula for the number of
unique pairs of gateways:
Total links between gateways
Now put the givern value “6” in this formula . .
The total number of links required to connect the 6 gateways in mesh topology is 15
