> 0ZY(`
2`/0DArialNew $$`<0z[ 0"DTimes New Roman0z[ 0@.
@n?" dd@ @@``HHF89:;<=>?@ABCDEFGHI0AA3@g45d5dz[ 0ppp@ʚ;&)ʚ;<4dddd|- 0Ը0___PPT10
___PPT9/0123564?
%
#- Physical Layer - Data Link Layer$#(Exercises on
"
<3
Exercise 1QA noiseless 4 kHz channel is sampled every 1 msec. What is the maximum data rate?R" R-!3/
Exercise 2If a binary signal is sent over a 3 kHz channel whose signal-to-noise ratio is 20dB, what is the maximum achievable data rate?
What is the maximum achievable data rate if we used 3 signal levels instead of 2 signal levels?" Z60
Exercise 38Three packet switching networks each contain n nodes. The first network has a star topology with a central switch, the second is a bi-directional ring, and the third is fully interconnected, with a wire from every node to every other node.
What are the best, average, and worst case transmission paths in hops? *" H" 981
Exercise 4JWhat signal-to-noise ratio is needed to put a T1 carrier on a 50-kHz line?K" ZK92
Exercise 5In most networks, the data link layer handles transmission errors by requesting damaged frames to be re-transmitted. If the probability of a frame's being damaged is p, what is the mean number of transmissions required to send a frame if the acknowledgements are never lost? 0" m<3
Exercise 6Imagine that you have trained your dog to carry a box of three 8mm Exabyte tapes. These tapes each contain 7 gigabytes. The dog can travel to your side, wherever you may be, at 18 km/hr.
For what range of distances does your dog have a higher data rate than a 155-Mbps ATM line? " ZC@5
Exercise 7sIf the bit string 0111101111101111110 is bit stuffed using the frame delimiter 01111110, what is the output string?t" ZtA6
Exercise 8*What is the Hamming code of 0110101100010?+" Z+=4
Exercise 9^What is the remainder obtained by dividing x^7 + x^5 + 1 by the generator polynomial x^3 + 1 ?_" Z_/457:;>?BC@
` ` ̙33` 333MMM` ff3333f` f` f` 3>?" dd@,|?" dd@ p " `@ P`p n?" dd@ @@``PN @ ` `p@@4,@(
68 "
T Click to edit Master title style!
!$
0 "
RClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level!
S
0̍ "``
F*0
04 "`
H*0
0 "`
H*0H
0h ? ̙33F0___PPT10.%ntD___PPT92 P2 p2 2 Tannenbaum
0zr
(
0̻; 18
;
P*
0; f 8;
R*
d
c$ ?4d
;
0|; ;
RClick to edit Master text styles
Second level
Third level
Fourth level
Fifth level!
S
6; '1_ ;
P*
6; 'f _;
R*
H
0bf@ ? 3380___PPT10.?ڛ $0$(
r
S0"_ 3"
r
SԱ"gL"
H
0h ? 3380___PPT10.%ip8$
`$(
r
S<7
r
Sߟ4Iq
H
0h ? ̙3380___PPT10.%R
0(
x
c$AU
#
x
c$8EU4IU
H
0h ? ̙33___PPT10i.%R+D=' =
@B +0
0(
x
c$QU
U
x
c$(>U4U
H
0h ? ̙3380___PPT10.%R
0(
x
c$;
;
x
c$F4IY;
H
0h ? ̙33___PPT10i.%R+D=' =
@B +0
0(
x
c$D5
`
x
c$\F4
H
0h ? ̙3380___PPT10.%R
0(
x
c$#
x
c$|`4I#
H
0h ? ̙33___PPT10i.%R+D=' =
@B +
`0(
x
c$F
F
x
c$)F4IYF
H
0h ? ̙33___PPT10i.%R+D=' =
@B +
0(
x
c$HvF
F
x
c$4.F4IYF
H
0h ? ̙33___PPT10i.%R+D=' =
@B +
@0(
x
c$(
x
c$cF4I
H
0h ? ̙33___PPT10i.%R+D=' =
@B +
0(
^
S4d
;}
c$;;
If we assume a finite number of discrete signals per level, say "2" then:
maximum data rate = 2 H log_2(V)
Where: H = 4,000, V = 2
maximum data rate = 2 * 4,000 * log_2(2) = 12.7 kbps
A better answer is that in general, a noiseless channel can carry an arbitrarily large amount of information, no matter how often it is sampled. Just send a lot of data per sample. The key word here is "noiseless." With a normal 4 kHz channel, the Shannon limit would not allow this.
KH
0bf@ ? 3380___PPT10.?m /
0
(
d
c$4d
U
s*DQUU
Shannon's theorem says:
maximum data rate = H log_2(1 + S/N) bps
H = 3000
20dB = 10 log_10(S/N)
S/N = 100
maximum data rate = 3000 * log_2(1 + 100) = 19.5 kbps
Nyquist's theorem says:
maximum data rate = 2 H log_2(V) bps
H = 3000
V = 2
maximum data rate = 2 * 3000 * log_2(2) = 6000 bps
Therefore, the maximum data rate is limited by Nyquist's theorem to be 6000bps.
If the signal level was 3, then we could do :
maximum data rate = 2 H log_2(V) bps
H = 3000
V = 2
maximum data rate = 2 * 3000 * log_2(3) = 6000 * log_2(3) bps !Z!, H
0bf@ ? 3380___PPT10.?m 0
0LD(
d
c$4d
U8
s*ĹFU
The three networks have the following properties:
star: best = 2, average = 2, worst = 2
ring: best = 1, average = n/4, worst = n/2
complete: best = 1, average = 1, worst = 1 H
0bf@ ? 3380___PPT10.?m P1
0`(
d
c$4d
;
s*F;
JTo send a T1 signal we need H log_2(1+S/N) = 1,544,000, with H = 50,000.
So:
50,000 * log_2(1 + S/N) = 1,544,000 log_2(1 + S/N) = 31
S/N = 2^31 1
Since S/N ratio is reported in decibles, the ration of 10log base 10 (S/N) is given:
10 log_10 (2^31 - 1) = 93 dB MH
0bf@ ? 3380___PPT10.?m &2
06(
d
c$4d
s*|z
dThe probability, Pk, of a frame requiring exactly k transmissions is the probablity of the first k-1 attempts failing, p^^(k-1), times
the probability of the k-th transmission succeeding, (1-p).
The mean number of transmissions is then just:
sum from k = 1 to infinity of kPk
which reduces to:
sum from k = 1 to infinity of k(1-p)p^^(k-1) = 1 / (1 - p) He2.;P6
LpOH
0bf@ ? 3380___PPT10.?m 3
0,$0(
d
c$4d
`
s*`
The dog can carry 21 gigabytes, or 168 gigabits.
A speed of 20 km/hour equals 0.005 km/sec.
The time to travel x km is x/0.005 = 200x sec, giving a data rate of 168/200x Gpbs or 840/x Mbps.
For x < 5/4 km, the dog has a higher rate than an ATM line.lq#
DMH
0bf@ ? 3380___PPT10.?m #4
0P3(
d
c$4d
F
s*FF
10110111
------------
1001 |10100001000
1001
----
1100
1001
----
1010
1001
----
1110
1001
----
1110
1001
----
1110
1001
----
111
H
0bf@ ? 3380___PPT10.?m W5
0pg(
d
c$4d
F
s*hCF
Q#Ans: 01111011111001111101001111110 !H
0bf@ ? 3380___PPT10.?m L6
0\(
d
c$4d
s*$!
FAns: 000111011011000110 H
0bf@ ? 3380___PPT10.?m r`@#&2 <(<%@*D-/GK19PS_46VOY?
[En(`
2`/0DArialNew h۠<$0<z[ 04DTimes New Roman<$0<z[ 04@.
@n?" dd@ @@``HHF89:;<=>?Root EntrydO)@rjWCurrent UserJSummaryInformation(,PowerPoint Document(89:;<=>?@ABCDEFGHI0AA3@g4BdBdTz[ 0~ppp@ʚ;&k3ʚ;<4dddd|- 0l0___PPT10
___PPT9|/0123564?
%
#- Physical Layer - Data Link Layer$#(Exercises on
"
<3
Exercise 1QA noiseless 4 kHz channel is sampled every 1 msec. What is the maximum data rate?R" R-!3/
Exercise 2If a binary signal is sent over a 3 kHz channel whose signal-to-noise ratio is 20dB, what is the maximum achievable data rate?
What is the maximum achievable data rate if we used 3 signal levels instead of 2 signal levels?" Z60
Exercise 38Three packet switching networks each contain n nodes. The first network has a star topology with a central switch, the second is a bi-directional 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? (" H" 981
Exercise 4JWhat signal-to-noise ratio is needed to put a T1 carrier on a 50-kHz line?K" ZK92
Exercise 5In most networks, the data link layer handles transmission errors by requesting damaged frames to be re-transmitted. If the probability of a frame's being damaged is p, what is the mean number of transmissions required to send a frame if the acknowledgements are never lost? *" m<3
Exercise 6Imagine that you have trained your dog to carry a box of three 8mm Exabyte tapes. These tapes each contain 7 gigabytes. The dog can travel to your side, wherever you may be, at 18 km/hr.
For what range of distances does your dog have a higher data rate than a 155-Mbps ATM line? " ZC@5
Exercise 7sIf the bit string 0111101111101111110 is bit stuffed using the frame delimiter 01111110, what is the output string?t" ZtA6
Exercise 8*What is the Hamming code of 0110101100010?+" Z+=4
Exercise 9^What is the remainder obtained by dividing x^7 + x^5 + 1 by the generator polynomial x^3 + 1 ?_" Z_/457:;>?BC3
0>60(
d
c$4d
8*
s*\P88
The dog can carry 21 gigabytes, or 168 gigabits.
A speed of 20 km/hour equals 0.005 km/sec.
The time to travel x km is x/0.005 = 200x sec, giving a data rate of 168/200x Gpbs or 840/x Mbps.
For x < 5,4 km, the dog has a higher rate than an ATM line.lq#
D,1H
0bf@ ? 3380___PPT10.?m rt>3?
sOE(`
2`/0DArialNew $f`0z[ 0DTimes New Roman0z[ 0@.
@n?" dd@ @@``HH)89:;<=>?0AA3@g4;d;d z[ 0ppp@ʚ;^-ʚ;<4ddddL|- 08$0___PPT10
___PPT9/01?
%P- Physical Layer (Exercises on
"
<3
Exercise 1QA noiseless 4 kHz channel is sampled every 1 msec. What is the maximum data rate?R" R-!3/
Exercise 2If a binary signal is sent over a 3 kHz channel whose signal-to-noise ratio is 20dB, what is the maximum achievable data rate?
What is the maximum achievable data rate if we used 3 signal levels instead of 2 signal levels?" Z60
Exercise 38Three packet switching networks each contain n nodes. The first network has a star topology with a central switch, the second is a bi-directional 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? (" H" 981
Exercise 4JWhat signal-to-noise ratio is needed to put a T1 carrier on a 50-kHz line?K" ZK/p457:P0P(
r
SL_ 3L
r
SLgLL
$
0Lg tF>6___PPT9
v Solutions are in the slide notes!" ! H
0h ? 3380___PPT10.%ip8T1
0d(
d
c$4d
L
s* L
NTo send a T1 signal we need H log_2(1+S/N) = 1,544,000, with H = 50,000.
So:
50,000 * log_2(1 + S/N) = 1,544,000
log_2(1 + S/N) = 31
S/N = 2^31 1
Since S/N ratio is reported in decibles, the ration of 10log base 10 (S/N) is given:
10 log_10 (2^31 - 1) = 93 dB MH
0bf@ ? 3380___PPT10.?m r:v1?
gҟE^(`
2`/0DArialNew RomanTT.ܖ0ܖDTimes New RomanTT.ܖ0ܖ@.
@n?" dd@ @@``HH(0AA3@g4UdUdT>06ppp@ʚ;^-ʚ;<4dddd l0 $0___PPT10
___PPT9/01?
%P- Physical Layer (Exercises on
"
<3
Exercise 1QA noiseless 4 kHz channel is sampled everDocumentSummaryInformation8<89:;<=>?@ABCDEFGHI0AA3@g4BdBdTz[ 0~ppp@ʚ;&k3ʚ;<4dddd|- 0l0___PPT10
___PPT9|/0123564?
%
#- Physical Layer - Data Link Layer$#(Exercises on
"
<3
Exercise 1QA noiseless 4 kHz channel is sampled every 1 msec. What is the maximum data rate?R" R-!3/
Exercise 2If a binary signal is sent over a 3 kHz channel whose signal-to-noise ratio is 20dB, what is the maximum achievable data rate?
What is the maximum achievable data rate if we used 3 signal levels instead of 2 signal levels?" Z60
Exercise 38Three packet switching networks each contain n nodes. The first network has a star topology with a central switch, the second is a bi-directional 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? (" H" 981
Exercise 4JWhat signal-to-noise ratio is needed to put a T1 carrier on a 50-kHz line?K" ZK92
Exercise 5In most networks, the data link layer handles transmission errors by requesting damaged frames to be re-transmitted. If the probability of a frame's being damaged is p, what is the mean number of transmissions required to send a frame if the acknowledgements are never lost? *" m<3
Exercise 6Imagine that you have trained your dog to carry a box of three 8mm Exabyte tapes. These tapes each contain 7 gigabytes. The dog can travel to your side, wherever you may be, at 18 km/hr.
For what range of distances does your dog have a higher data rate than a 155-Mbps ATM line? " ZC@5
Exercise 7sIf the bit string 0111101111101111110 is bit stuffed using the frame delimiter 01111110, what is the output string?t" ZtA6
Exercise 8*What is the Hamming code of 0110101100010?+" Z+=4
Exercise 9^What is the remainder obtained by dividing x^7 + x^5 + 1 by the generator polynomial x^3 + 1 ?_" Z_/457:;>?BC*
0:(
^
S4d
c$8
0If we assume a finite number of discrete signals per level, say "2" then:
maximum data rate = 2 H log_2(V)
Where: H = 4,000, V = 2
maximum data rate = 2 * 4,000 * log_2(2) = 8 kbps
A better answer is that in general, a noiseless channel can carry an arbitrarily large amount of information, no matter how often it is sampled. Just send a lot of data per sample. The key word here is "noiseless." With a normal 4 kHz channel, the Shannon limit would not allow this.
K%H
0bf@ ? 3380___PPT10.?m r/\4o?
\sEn(`
2`/0DArialNew h۠<$0<z[ 04DTimes New Roman<$0<z[ 04@.
@n?" dd@ @@``HHFy 1 msec. What is the maximum data rate?R" R-!3/
Exercise 2If a binary signal is sent over a 3 kHz channel whose signal-to-noise ratio is 20dB, what is the maximum achievable data rate?
What is the maximum achievable data rate if we used 3 signal levels instead of 2 signal levels?" Z60
Exercise 3Oh+'0hp
(The Data Link LayerSteve ArmstrongTannenbaumRoberto Riggio37Microsoft PowerPoint@9%F@ntD%@p_jGg ]y--$xx--'@Times New Roman-. 2
A/-."System;-@Times New Roman-. 2
A5Physical Layer .-@Times New Roman-. 32
&/Exercises on
!"#$%&'()*+,-.JGI23456789:;<=>?@ABCDEF/HVKLMNOPQRSTU1]X[\^_
.-@Time&_Roberto RiggioRoberto RiggioSolutions are in the slide notes
.--2
&/Exercises on&_Roberto RiggioRoberto R՜.+,0
$On-screen Show East Texas Data Service1ArialTimes New RomanTannenbaum- Physical Layer Exercise 1Exercise 2Exercise 3Exercise 4Fonts UsedDesign Template
Slide TitlesiggioillaniDesign Template
8Three packet switching networks each contain n nodes. The first network has a star topology with a central switch, the second is a bi-directional 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? (" H" 981
Exercise 4JWhat signal-to-noise ratio is needed to put a T1 carrier on a 50-kHz line?K" ZK/p457:$00$(
r
SĪ_ 3
r
S$gL
H
0h ? 3380___PPT10.%ip8rծE1