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Computer Networks: Global Edition

Andrew S. Tanenbaum, Nick Feamster, David Wetherall

Chapter 2

The Physical Layer - all with Video Answers

Educators


Chapter Questions

02:03

Problem 1

Is an oil pipeline a simplex system, a half-duplex system, a full-duplex system, or none of the above? What about a river or a walkie-talkie-style communication?

Narayan Hari
Narayan Hari
Numerade Educator
02:14

Problem 2

What are the advantages of fiber optics over copper as a transmission medium? Is there any downside of using fiber optics over copper?

Ajay Singhal
Ajay Singhal
Numerade Educator
02:33

Problem 3

How much bandwidth is there in $0.1$ microns of spectrum at a wavelength of 1 micron?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:12

Problem 4

It is desired to send a sequence of computer screen images over an optical fiber. The screen is $3840 \times 2160$ pixels, each pixel being 24 bits. There are 50 screen images per second. What data rate is needed is needed?

Narayan Hari
Narayan Hari
Numerade Educator
00:56

Problem 5

In Fig. 2-5, the left-hand band is narrower than the others. Why?

Elizabeth Xu
Elizabeth Xu
Numerade Educator
01:02

Problem 6

Radio antennas often work best when the diameter of the antenna is equal to the wavelength of the radio wave. Reasonable antennas range from $1 \mathrm{~cm}$ to 1 meter in diameter. What frequency range does this cover?

Narayan Hari
Narayan Hari
Numerade Educator
02:00

Problem 7

Multipath fading is maximized when the two beams arrive 180 degrees out of phase. How much of a path difference is required to maximize the fading for a 100 -km-long 1-GHz microwave link?

Aja S
Aja S
Numerade Educator
02:42

Problem 8

A laser beam $1 \mathrm{~mm}$ wide is aimed at a detector $1 \mathrm{~mm}$ wide $100 \mathrm{~m}$ away on the roof of a building. How much of an angular diversion (in degrees) does the laser have to have before it misses the detector?

Naresh Bagrecha
Naresh Bagrecha
Numerade Educator
View

Problem 9

Compute the Fourier coefficients for the function $f(t)=t \quad(0 \leq t \leq 1)$.

Victor Salazar
Victor Salazar
Numerade Educator
00:46

Problem 10

Identify three physical properties that limit the maximum data rate of digital communication channels used in practice. Explain your answers.

Ronald Prasad
Ronald Prasad
Numerade Educator
01:24

Problem 11

A noiseless $10-\mathrm{kHz}$ channel is sampled every $1 \mathrm{msec}$. What is the maximum data rate?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
02:31

Problem 12

Is the Nyquist theorem true for high-quality single-mode optical fiber or only for copper wire?

Arpit Gupta
Arpit Gupta
Numerade Educator
01:34

Problem 13

Television channels are $6 \mathrm{MHz}$ wide. How many bits/sec can be sent if four-level digital signals are used? Assume a noiseless channel.

Keshav Singh
Keshav Singh
Numerade Educator
01:24

Problem 14

If a binary signal is sent over a $3-\mathrm{kHz}$ channel whose signal-to-noise ratio is $20 \mathrm{~dB}$, what is the maximum achievable data rate?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
01:06

Problem 15

You need to select a line code that will only be used to send the bit sequences 10101010 and 00111100 . Which of the lines codes shown in Fig. 2-14 is not a good candidate? Consider both bandwidth efficiency and clock recovery.

James Kiss
James Kiss
Numerade Educator
01:52

Problem 16

What is the minimum bandwidth needed to achieve a data rate of $B$ bits/sec if the signal is transmitted using NRZ, MLT-3, and Manchester encoding? Explain.

João Bravo
João Bravo
Numerade Educator
10:22

Problem 17

Prove that in $4 \mathrm{~B} / 5 \mathrm{~B}$ mapped data with the NRZI encoding, a signal transition will occur at least every four bit times.

Chris Trentman
Chris Trentman
Numerade Educator
00:52

Problem 18

A modem constellation diagram similar to Fig. 2-17 has data points at $(0,1)$ and $(0,2)$. Does the modem use phase modulation or amplitude modulation?

Hast Aggarwal
Hast Aggarwal
Numerade Educator
02:23

Problem 19

In a constellation diagram, all the points lie on a circle centered on the origin. What kind of modulation is being used?

Arpit Gupta
Arpit Gupta
Numerade Educator
01:40

Problem 20

Ten signals, each requiring $4000 \mathrm{~Hz}$, are multiplexed onto a single channel using FDM. What is the minimum bandwidth required for the multiplexed channel? Assume that the guard bands are $400 \mathrm{~Hz}$ wide.

Narayan Hari
Narayan Hari
Numerade Educator
01:16

Problem 21

Suppose that $A, B$, and $C$ are simultaneously transmitting 0 bits, using a CDMA system with the chip sequences of Fig. 2-22(a). What is the resulting chip sequence?

Shelby Mohamed
Shelby Mohamed
Numerade Educator
01:31

Problem 22

In the discussion about orthogonality of CDMA chip sequences, it was stated that if $\mathbf{S} \cdot \mathbf{T}=0$ then $\mathbf{S} \cdot \overline{\mathbf{T}}$ is also 0 . Prove this.

IL
Iris L.
Numerade Educator
03:52

Problem 23

Consider a different way of looking at the orthogonality property of CDMA chip se- quences. Each bit in a pair of sequences can match or not match. Express the orthogonality property in terms of matches and mismatches.

Chris Trentman
Chris Trentman
Numerade Educator
01:21

Problem 24

A CDMA receiver gets the following chips: $(-1+1-3+1-1-3+1+1)$. Assuming the chip sequences defined in Fig. 2-22(a), which stations transmitted, and which bits did each one send?

Clarissa Noh
Clarissa Noh
Numerade Educator
01:07

Problem 25

In Fig. 2-22, there are four stations that can transmit. Suppose four more stations are added. Provide the chip sequences of these stations.

Linh Vu
Linh Vu
Numerade Educator
01:16

Problem 26

A base station schedules a single slot for devices A and B to send data using their corresponding chip sequences from Fig. 2-22. During this time, other stations remain silent. Due to noise, some of the chips are lost. The base station receives the following sequence: $(0,0, ?, 2, ?, ?, 0,-2)$. What are the bit values transmitted by stations $\mathrm{A}$ and B?

Shelby Mohamed
Shelby Mohamed
Numerade Educator
01:19

Problem 27

How many end office codes were there pre-1984, when each end office was named by its three-digit area code and the first three digits of the local number? Area codes started with a digit in the range $2-9$, had a 0 or 1 as the second digit, and ended with any digit. The first two digits of a local number were always in the range $2-9$. The third digit could be any digit.

Hunza Gilgit
Hunza Gilgit
Numerade Educator
02:41

Problem 28

A simple telephone system consists of two end offices and a single toll office to which each end office is connected by a 1-MHz full-duplex trunk. The average telephone is used to make four calls per 8-hour workday. The mean call duration is $6 \mathrm{~min}$. Ten percent of the calls are long distance (i.e., pass through the toll office). What is the maximum number of telephones an end office can support? (Assume $4 \mathrm{kHz}$ per circuit.) Explain why a telephone company may decide to support a lesser number of telephones than this maximum number at the end office.

Jodi Folley
Jodi Folley
Numerade Educator
04:32

Problem 29

A regional telephone company has 15 million subscribers. Each of their telephones is connected to a central office by a copper twisted pair. The average length of these twisted pairs is $10 \mathrm{~km}$. How much is the copper in the local loops worth? Assume that the cross section of each strand is a circle $1 \mathrm{~mm}$ in diameter, the density of copper is $9.0 \mathrm{grams} / \mathrm{cm}^{3}$, and that copper sells for $\$ 6$ per kilogram.

James Irizarry
James Irizarry
Numerade Educator
01:52

Problem 30

What is the maximum bit rate achievable in a V.32 standard modem if the baud rate is 9600 and no error correction is used?

João Bravo
João Bravo
Numerade Educator
04:12

Problem 31

The cost of a fast microprocessor has dropped to the point where it is now possible to put one in each modem. How does that affect the handling of telephone line errors? Does it negate the need for error checking/correction in layer $2 ?$

Yi Chun Lin
Yi Chun Lin
Washington University in St Louis
01:40

Problem 32

An ADSL system using DMT allocates $3 / 4$ of the available data channels to the downstream link. It uses QAM-64 modulation on each channel. What is the capacity of the downstream link?

Narayan Hari
Narayan Hari
Numerade Educator
01:14

Problem 33

Why has the PCM sampling time been set at $125 \mu \mathrm{sec}$ ?

Vysakh M
Vysakh M
Numerade Educator
00:31

Problem 34

What signal-to-noise ratio is needed to put a T1 carrier on a $200-\mathrm{kHz}$ line?

Gopal Sharma
Gopal Sharma
Numerade Educator
01:24

Problem 35

Compare the maximum data rate of a noiseless $4-\mathrm{kHz}$ channel using
(a) Analog encoding (e.g., QPSK) with 2 bits per sample.
(b) The T1 PCM system.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
07:46

Problem 36

If a Tl carrier system slips and loses track of where it is, it tries to resynchronize using the first bit in each frame. How many frames will have to be inspected on average to resynchronize with a probability of $0.001$ of being wrong?

Derrick Hanson
Derrick Hanson
Numerade Educator
04:55

Problem 37

What is the percent overhead on a T1 carrier? That is, what percent of the $1.544$ Mbps are not delivered to the end user? How does it relate to the percent overhead in $\mathrm{OC}-1$ or $\mathrm{OC}-768$ lines?

Narayan Hari
Narayan Hari
Numerade Educator
03:14

Problem 38

SONET clocks have a drift rate of about 1 part in $10^{9}$. How long does it take for the drift to equal the width of 1 bit? Do you see any practical implications of this calculation? If $s 0$, what?

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
10:37

Problem 39

In Fig. 2-35, the user data rate for $\mathrm{OC}-3$ is stated to be $148.608 \mathrm{Mbps}$. Show how this number can be derived from the SONET OC-3 parameters. What will be the gross, SPE, and user data rates of an OC-3072 line?

Oswaldo Jiménez
Oswaldo Jiménez
Numerade Educator
02:09

Problem 40

To accommodate lower data rates than STS-1, SONET has a system of virtual tributaries (VTs). A VT is a partial payload that can be inserted into an STS-1 frame and combined with other partial payloads to fill the data frame. VT15 uses 3 columns, VT2 uses 4 columns, VT3 uses 6 columns, and VT6 uses 12 columns of an STS-1 frame. Which VT can accommodate
(a) A DS-1 service (1.544 Mbps)?
(b) European CEPT-1 service $(2.048 \mathrm{Mbps})$ ?
(c) A DS-2 service (6.312 Mbps)?

James Kiss
James Kiss
Numerade Educator
04:55

Problem 41

What is the available user bandwidth in an $\mathrm{OC}-12 \mathrm{c}$ connection?

Narayan Hari
Narayan Hari
Numerade Educator
03:48

Problem 42

What is the difference, if any, between the demodulator part of a modem and the coder part of a codec? (After all, both convert analog signals to digital ones.)

Jennifer Stoner
Jennifer Stoner
Numerade Educator
02:24

Problem 43

Three packet-switching networks each contain $n$ nodes. The first network has a star topology with a central switch, the second is a (bidirectional) ring, and the third is fully interconnected, with a wire from every node to every other node. What are the best-, average-, and worst-case transmission paths in hops?

James Kiss
James Kiss
Numerade Educator
01:00

Problem 44

Compare the delay in sending an $x$-bit message over a $k$-hop path in a circuit-switched network and in a (lightly loaded) packet-switched network. The circuit setup time is $s$ sec, the propagation delay is $d$ sec per hop, the packet size is $p$ bits, and the data rate is $b$ bps. Under what conditions does the packet network have a lower delay? Also, explain the conditions under which a packet-switched network is preferable to a circuit-switched network.

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
01:00

Problem 45

Suppose that $x$ bits of user data are to be transmitted over a $k$-hop path in a packet-switched network as a series of packets, each containing $p$ data bits and $h$ header bits, with $x>p+h$. The bit rate of the lines is $b$ bps and the propagation delay is negligible. What value of $p$ minimizes the total delay?

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
01:13

Problem 46

In a typical mobile phone system with hexagonal cells, it is forbidden to reuse a frequency band in an adjacent cell. If 840 frequencies are available, how many can be used in a given cell?

Mayukh Banik
Mayukh Banik
Numerade Educator
04:05

Problem 47

The actual layout of cells is seldom as regular that as shown in Fig. 2-39. Even the shapes of individual cells are typically irregular. Give a possible reason why this might be. How do these irregular shapes affect frequency assignment to each cell?

Ayushi Balan
Ayushi Balan
Numerade Educator
02:21

Problem 48

Make a rough estimate of the number of PCS microcells $100 \mathrm{~m}$ in diameter it would take to cover San Francisco (120 square $\mathrm{km}$ ).

Linh Vu
Linh Vu
Numerade Educator
01:38

Problem 49

Sometimes when a mobile user crosses the boundary from one cell to another, the current call is abruptly terminated, even though all transmitters and receivers are functioning perfectly. Why?

VS
Vivek Singh
Numerade Educator
09:04

Problem 50

At the low end, the telephone system is star shaped, with all the local loops in a neighborhood converging on an end office. In contrast, cable television consists of a single long cable snaking its way past all the houses in the same neighborhood. Suppose that a future TV cable were 10-Gbps fiber instead of copper. Could it be used to simulate the telephone model of everybody having their own private line to the end office? If so, how many one-telephone houses could be hooked up to a single fiber?

Angela Guo
Angela Guo
Numerade Educator
09:04

Problem 51

A cable company decides to provide Internet access over cable in a neighborhood consisting of 5000 houses. The company uses a coaxial cable and spectrum allocation allowing $100 \mathrm{Mbps}$ downstream bandwidth per cable. To attract customers, the company decides to guarantee at least 2 Mbps downstream bandwidth to each house at any time. Describe what the cable company needs to do to provide this guarantee.

Angela Guo
Angela Guo
Numerade Educator
01:07

Problem 52

Using the spectral allocation of Fig. 2-46 and the information given in the text, how many Mbps does a cable system allocate to upstream and how many to downstream?

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
View

Problem 53

How fast can a cable user receive data if the network is otherwise idle? Assume that the user interface is
(a) 10 -Mbps Ethernet
(b) 100-Mbps Ethemet
(c) 54-Mbps Wireless.

James Kiss
James Kiss
Numerade Educator
06:46

Problem 54

The 66 low-orbit satellites in the Iridium project are divided into six necklaces around the earth. At the altitude they are using, the period is 90 minutes. What is the average interval for handoffs for a stationary transmitter?

Donald Albin
Donald Albin
Numerade Educator
05:56

Problem 55

Consider a satellite at the altitude of geostationary satellites but whose orbital plane is inclined to the equatorial plane by an angle $\phi$. To a stationary user on the earth's surface at north latitude $\phi$, does this satellite appear motionless in the sky? If not, describe its motion.

Linda Winkler
Linda Winkler
Numerade Educator
02:41

Problem 56

Calculate the end-to-end transit time for a packet for both GEO (altitude: $35,800 \mathrm{~km}$ ), MEO (altitude: $18,000 \mathrm{~km}$ ), and LEO (altitude: $750 \mathrm{~km}$ ) satellites.

Andy Chen
Andy Chen
Numerade Educator
01:03

Problem 57

What is the latency of a call originating at the North Pole to reach the South Pole if the call is routed via Iridium satellites? Assume that the switching time at the satellites is 10 microseconds and earth's radius is $6371 \mathrm{~km}$.

- -
- -
Numerade Educator
02:25

Problem 58

How long will it take to transmit a 1-GB file from one VSAT to another using a hub as shown in Fig. 2-50? Assume that the uplink is $1 \mathrm{Mbps}$, the downlink is $7 \mathrm{Mbps}$, and circuit switching is used with $1.2$ sec circuit setup time.

Shelby Mohamed
Shelby Mohamed
Numerade Educator
02:53

Problem 59

Calculate the transmit time in the previous problem if packet switching is used instead. Assume that the packet size is $64 \mathrm{~KB}$, the switching delay in the satellite and hub is 10 microseconds, and the packet header size is 32 bytes.

Samriddhi Singh
Samriddhi Singh
Numerade Educator
03:17

Problem 60

Multiplexing STS-1 multiple data streams, called tributaries, plays an important role in SONET. A $3: 1$ multiplexer multiplexes three input STS-1 tributaries onto one output STS-3 stream. This multiplexing is done byte for byte. That is, the first three output bytes are the first bytes of tributaries 1,2, and 3 , respectively. The next three output bytes are the second bytes of tributaries 1,2 , and 3 , respectively, and so on. Write a program that simulates this $3: 1$ multiplexer. Your program should consist of five processes. The main process creates four processes, one each for the three STS-1 tributaries and one for the multiplexer. Each tributary process reads in an STS-1 frame from an input file as a sequence of 810 bytes. They send their frames (byte by byte) to the multiplexer process. The multiplexer process receives these bytes and outputs an STS-3 frame (byte by byte) by writing it to standard output. Use pipes for communication among processes.

Sriram Soundarrajan
Sriram Soundarrajan
Numerade Educator
03:06

Problem 61

Write a program to implement CDMA. Assume that the length of a chip sequence is eight and the number of stations transmitting is four. Your program consists of three sets of processes: four transmitter processes (to, $\mathrm{t} 1$, $\mathrm{t} 2$, and $\mathrm{t} 3$ ), one joiner process, and four receiver processes (ro, $\mathrm{r} 1, \mathrm{r} 2$, and $\mathrm{r} 3$ ). The main program, which also acts as the joiner process first reads four chip sequences (bipolar notation) from the standard input and a sequence of 4 bits (1 bit per transmitter process to be transmitted), and forks off four pairs of transmitter and receiver processes. Each pair of transmitter/receiver processes ( $t 0,0 ; t 1, r 1 ; 12, r 2 ; t 3, r 3$ ) is assigned one chip sequence and each transmitter process is assigned 1 bit (first bit to to, second bit to t1, and so on). Next, each transmitter process computes the signal to be transmitted (a sequence of 8 bits) and sends it to the joiner process. After receiving signals from all four transmitter processes, the joiner process combines the signals and sends the combined signal to the four receiver processes. Each receiver process then computes the bit it has received and prints it to standard output. Use pipes for communication between processes.

WZ
Wen Zheng
Numerade Educator