edited by
48,138 views
126 votes
126 votes

Frames of $\text{1000 bits}$ are sent over a $10^6$ $\text{bps}$ duplex link between two hosts. The propagation time is $\text{25 ms}$. Frames are to be transmitted into this link to maximally pack them in transit (within the link).

What is the minimum number of bits $(I)$ that will be required to represent the sequence numbers distinctly? Assume that no time gap needs to be given between transmission of two frames.

  1. $I=2$
  2. $I=3$
  3. $I=4$
  4. $I=5$
edited by

18 Answers

4 votes
4 votes

Duplex simply means both sender and receiver can send and receive the signals which is bydefault as we know.

Tx = 1ms (1 frame data put on cable) 

Tp = 25ms (25 frame data can be put on cable in this time if we fully utilize the link).

Total time : 1 + 25 = 26 ms (from frist bit of of first frame put on cable to last bit of frame reached to receiver)

So to fully utilize the link we must use the link for 26 ms (26 frames need to transmit)

frames numbered as 0,1,2,3,...25 thus we need 26 different sequence numbers

therefore bits rewuired for sequence number = ceil(log 26) = 5

4 votes
4 votes

For Half Duplex, Capacity of the channel = BW * Tp
So we get capacity = $10^6$ b/s * 25 * 10 ^ -3 s
                               = 25 * $10^3 bits$

so a channel can contain 25 * $10^3 bits$ but we are sending only frames of 1000 bits
Therefore, the total no. of frames we are sending with its full channel capacity = 25 * 1000/1000 = 25 frames.
For this much frames the seq.numbers nedded are 25.
And Seq.no.bits required are $Ceil(\log_{2}25)$ = 5 bits

edited by
4 votes
4 votes

5 bits

1 votes
1 votes
Propagation time is given as 25 ms.

Bandwidth = 106 bps.

So, to fully utilize the channel, we must send 106 bits into the channel in a second, which will be 1000 frames per second as each frame is 1000 bits. Now, since the propagation time is 25 ms, to fully pack the link we need to send at least 1000 * 25 * 10-3 = 25 frames. Since, to represent 25 frames we need 25 distinct index numbers. Thus, minimum no. of bits required to do this will be 5 (2^5=32) as 4 will not be enough (2^4=16, not enough to represent 25 distinct no.)
Answer:

Related questions

20 votes
20 votes
5 answers
5
Kathleen asked Sep 22, 2014
8,375 views
In which one of the following page replacement policies, Belady's anomaly may occur?FIFOOptimalLRUMRU
34 votes
34 votes
7 answers
6
Kathleen asked Sep 22, 2014
20,214 views
$$S \to aSa \mid bSb\mid a\mid b$$The language generated by the above grammar over the alphabet $\{a,b\}$ is the set of:all palindromesall odd length palindromesstrings t...
27 votes
27 votes
4 answers
8
Kathleen asked Sep 21, 2014
33,743 views
The message $11001001$ is to be transmitted using the CRC polynomial $x^3 +1$ to protect it from errors. The message that should be transmitted is:$11001001000$$110010010...