W09 314 extra credit for HW 09 solution

W09 314 extra credit for HW 09 solution - 


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Unformatted text preview: 
 Student’s
name
________SOLUTION__________







 Discussion
section
#
_______


 


























(Last,
First,
write
legibly,
use
ink)











































 (use
ink)
 Instructor
is
not
responsible
for
grading
and
entering
scores
for
HW
papers
lacking
 clear
information
in
the
required
fields
above
 
 EECS

314

 Winter
2009

 Extra
credit
assignment
for
HW
9
due
Tuesday
April
7
 
 
 Extra
credit
 Problem
1
(40
 points)
 Using
the
7‐segment
 display,
determine
which
 of
the
switches
should
be
 closed
in
order
to
display
 the
“equation”
Pi
=
3.14
 as
shown
here: For
reference,
the
first
two
rows
read
8
and
2.
 Character
 8
 2
 P
 i
 =
 3
 1
 4
 
 
 A
 1
 1
 1 0 B
 1
 1 1
 C
 1
 0
 0 0 D
 1
 1
 0 0 E
 1
 1 1
 F
 1
 0
 0 1 G
 1
 1
 1 0 0

 1 



 


 


 

 
 


 
 
 
 
 Ignore
the
decimal
point.
List
each
closed
switch
as
“1”
and
each
open
switch
as
“0”.
 1 0

 0 0 0 0 
 1 1 1 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 ©
2009
Alexander
Ganago

 Page
1
of
4
 
 Student’s
name
__SOLUTION__________________







 Discussion
section
#
_______


 


























(Last,
First,
write
legibly,
use
ink)











































 (use
ink)
 Instructor
is
not
responsible
for
grading
and
entering
scores
for
HW
papers
lacking
 clear
information
in
the
required
fields
above
 
 EECS

314

 Winter
2009

 Extra
credit
assignment
for
HW
9
due
Tuesday
April
7
 
 
 Extra
credit
Problem
2
 
(40
points)
 An
important
characteristics
of
sampling
is
the
bit
rate,
usually
expressed
in
 kilobits/second,
or
kbit/sec,
which
is
calculated
for
stereo
recording
as
the
product

 16 bits/sample * 44,000 samples/second * 2 channels/1000 bits/kilobit bits/sample
×
number
of
samples/second
×
2
channels
/
1000
bits/kilobit
 Calculate
the
bit
rate
for
CD
recording
with
16‐bit
resolution.

 
 Your
answer:
__________1408__________
kbit/sec
for
16‐bit
CD
recording
 
 Compare
your
result
with
the
popular
MP3
standard
128
kbit/sec:
calculate
the
 ratio
of
bit
rates
in
CD
and
MP3
recordings.

 1408/128=11 
 

 Your
answer:
the
ratio
of
bit
rates
(CD/MP3)
equals
______11_______________
 Assume
a
blank
disk
capacity
of
700
MB,
calculate
the
duration
of
music
recordings
 in
MP3
format
that
can
fit
on
that
disk.
Express
your
result
in
seconds,
as
well
as
in
 hours
and
minutes
(rounded
to
a
single
minute).
 1 sec/128 kbit * 1 kbit/1000 bit * 8 bits/byte * 700e6 bytes = 43750 sec 
 _______43750_________
seconds,
or
_____12_________
hours
and
__15____
minutes.
 

Show
your
work.
Use
separate
pages
as
needed.

 Your
answer:
a
700
MB
disk
can
hold
the
MP3
recordings
of
music
that
plays
for

 ©
2009
Alexander
Ganago

 Page
2
of
4
 
 Student’s
name
__SOLUTION_________________







 Discussion
section
#
_______


 

























(Last,
First,
write
legibly,
use
ink)











































 (use
ink)
 Instructor
is
not
responsible
for
grading
and
entering
scores
for
HW
papers
lacking
 clear
information
in
the
required
fields
above
 
 EECS

314

 Winter
2009

 Extra
credit
assignment
for
HW
9
due
Tuesday
April
7
 
 
 Extra
credit
Problem
3
 
(20
points)
 You
have
to
measure
the
amount
of
liquid
in
a
cylindrical
tank
 that
has
30,000
gal
capacity,
by
monitoring
the
height
H
with
a
 sensor.

 
 Given
that
the
maximal
error
should
not
exceed
10
gal,
you
will
 choose
an
A/D
converter
with
at
least
__12___
bits.
 
 Choose
the
minimal
number
of
bits
that
satisfies
the
 requirement.

 Show
your
work.
 
30000/(2N-1) < 10 
 

 
 N = 11.4, so rounding up gives N=12 Extra
credit
Problem
5
 Voltage
that
varies
between
‐25
V
and
+25
V
is
converted
into
binary
numbers
using
 an
8‐bit
A/D
converter.
The
maximal
error
of
this
digital
representation
(=
LSB)
is
 about
…
__195__
mV.
 
(20
points)
 (25V- -25V)/(2 8 -1)=50V/255=195mV 50V/(214 -1)=50/16383=3mV Show
your
work.
 
 Repeat
for
a
14‐bit
AD
converter.

 The
maximal
error
of
this
digital
representation
(=
LSB)
is
about
…
___3_
mV.
 
 ©
2009
Alexander
Ganago

 Page
3
of
4
 
 Student’s
name
___SOLUTION_______________







 Discussion
section
#
_______


 


























(Last,
First,
write
legibly,
use
ink)











































 (use
ink)
 Instructor
is
not
responsible
for
grading
and
entering
scores
for
HW
papers
lacking
 clear
information
in
the
required
fields
above
 
 EECS

314

 Winter
2009

 Extra
credit
assignment
for
HW
9
due
Tuesday
April
7
 
 
 Decimal‐to‐Binary
conversion

 Extra
credit
Problem
6
 
 9710
=
__11000012____________
 Convert
the
decimal
numbers
to
binary:
 
(20
points)
 17610
=
__101100002__________
 
 Extra
credit
Problem
7
 176 is made up of 27, 25, and 2 4 


 Show
your
work.
 
 
97 is made up of 2 6 , 25 , and 20 
(20
points)
 Convert
the
binary
numbers
to
decimal:

 
 
 10111002
=
_____92___________
 1*26+ 0*25+ 1*24+ 1*23+ 1*22+ 0*21+ 0*20=92 Show
your
work.
 1*2 6+ 1*2 5+ 0*24+ 1*23+ 1*22+ 0*21+ 0*20=108 
 
 
 11011002
=
_____108___________
 ©
2009
Alexander
Ganago

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4
of
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This note was uploaded on 10/28/2009 for the course EECS 314 taught by Professor Ganago during the Winter '07 term at University of Michigan.

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