W09 314 HW09 all - EECS 314 Winter 2009 Homework set 9...

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Unformatted text preview: EECS 314 Winter 2009 Homework set 9 Student’s name ___________________________ 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 Problem
1

 
 Codes
in
digital
circuits

 (40
points)
 In
the
table
below,
write
ASCII
codes
for
U
of
M
1817
(do
not
skip
the
spaces).

 For
reference,
the
first
two
rows
read
capital
A
and
B.
The
second
line
is
left
blank
 for
your
notes.

 Look
up
the
complete
set
of
codes
at
http://www.ascii‐code.com/
 
 Character
 A
 B
 
 U
 (space)
 
 
 
 0
 0
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1
 1
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0
 0
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ASCII
code
 0
 0
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0
 0
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0
 0
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0
 1
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1
 0
 o
(lower
case)
 
 f
(lower
case)
 
 (space)
 M
 (space)
 1
 8
 1
 7
 
 
 
 
 
 
 
 
 
 
 
 
 © 2009 Alexander Ganago Page 1 of 1 EECS 314 Winter 2009 Homework set 9 Student’s name ___________________________ 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 Problem
2

 Memory
required
for
data
storage

 (40
points)
 The
Big
Picture

 As
you
know
from
lecture
notes,
music
on
CD
is
recorded
with
16‐
or
20‐bit
 resolution,
at
the
sampling
rate
of
~
44
kHz.
As
you
know
from
reading
the
labels,
a
 blank
CD
has
the
capacity
of
700
MB
(megabytes;
1
Byte
=
8
bits;
1
MB
~
106
Bytes)
 and
is
rated
for
80
minutes
of
music
recording.
In
this
Problem,
you
will
“put
2
and
2
 together”
in
order
to
see
whether
all
of
the
above
numbers
make
sense.


 
 The
Assignment
 Assume
that
the
music
is
recorded
in
two
channels
(stereo
=
left
and
right)
that
have
 the
same
resolution
of
16
bits
and
the
same
sampling
rate
of
44
kHz.
Calculate
the
 amount
of
memory
in
MB
required
to
record
a
song
that
lasts
2
minutes
and
48
 seconds.

 Your
answer:
_____________________
MB

 Repeat
for
20‐
bit
recording:
 Your
answer:
_____________________
MB

 Assume
that
a
blank
CD
has
the
capacity
of
700
MB.
Calculate
how
many
minutes
of
 music
can
be
stored
on
the
CD.

 Your
answer:
T
=
_______________________
minutes
on
CD
 Repeat
for
20‐
bit
recording:
 
 If
your
answer
above
is
less
than
80
minutes,
it
means
that
a
data
compression
 algorithm
is
used
to
record
the
data
on
music
CDs.
The
compression
can
be
easily
 quantified:
for
example,
if
you
estimate
the
needed
memory
as
1
MB
and
the
actual
 record
requires
only
0.8
MB,
then
the
compression
ratio
equals
1/.8
=
1.25,
which
is
 very
modest
compared
to
that
used
in
MP3
technology.

 Discuss
your
answer:
if
you
found
T
>
80
minutes,
no
compression
is
needed.
If,
 however,
you
found
T
<
80
minutes,
compression
is
needed,
and
you
are
asked
to
 calculate
the
compression
ratio.

 Your
answer
on
compression:
_______________________________________________

 
 Show
your
work.
Use
additional
pages
as
needed.

 © 2009 Alexander Ganago Page 1 of 1 Your
answer:
______________
minutes
on
CD
 EECS 314 Fall 2008 Homework set 9 Student’s name ___________________________ 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 Problem
3

 Analog‐to‐Digital
Conversion
(ADC)
(40
points)
 Using
a
temperature
sensor
and
an
8‐bit
Analog‐to‐Digital
Converter
(ADC),
 students
built
a
thermometer
for
measuring
the
temperature
of
water
boiling
under
 various
pressures.
The
table
below
lists
the
two
reference
points.
 
 Temperature,
ºF
 ADC
output
(binary)
 180
 230
 
 
 
 00000000
 11111111
 00100100
 10100101
 Δmin=00000001
 Comment
 Lowest
temperature
 Highest
temperature
 T1
to
be
found
 T2
to
be
found
 ΔTmin
=
error,

 corresponding
to
LSB
 ΔTmax,

 corresponding
to
MSB
 
 Δmax=10000000
 Assume
that
the
temperature
sensor
is
linear.
Calculate
the
two
temperatures
T1
 and
T2,
which
correspond
to
the
ADC
outputs
listed
in
the
table.
Also,
calculate
the
 resolution,
or
error
of
temperature
measurements,
which
equals
the
Least
 Significant
Bit
(LSB),
and
the
change
of
temperature
that
equals
the
Most
Significant
 Bit
(MSB).

 Write
your
results
in
the
table
above.

 Show
your
work
below
and/or
on
separate
pages.

 © 2008 Alexander Ganago Page 1 of 1 EECS 314 Winter 2009 Homework set 9 Student’s name ___________________________ 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 Problem 4 Analog-to-Digital Conversion (ADC) circuit (60 points) Assume that the analog signal sketched here is fed into the AD converter shown on the diagram below, with VREF = 8 V. On the sketch, draw horizontal lines that correspond to sample-and-hold circuit output, assuming that the sampling is done at the beginning of each time interval T1, T2, etc. Note that sampling itself does not lead to rounding down. Analyze how the AD circuit works: show detailed calculations of the binary outputs D0, D1, D2 for the time interval T8 (below and/or on additional pages). Your answers: D0 = _______ D1 = _______ D2 = _______ Continued on the next page © 2009 Alexander Ganago Page 1 of 2 EECS 314 Winter 2009 Homework set 9 Student’s name ___________________________ 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 Problem 4, continued Based on your circuit analysis above, calculate the binary outputs D0, D1, D2 obtained during time intervals T1 through T8 (show your work below and/or on additional pages) and draw the digital waveforms on the grid: © 2009 Alexander Ganago Page 2 of 2 EECS 314 Winter 2009 Homework set 9 Student’s name ___________________________ 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 Problem
5
 Digital‐to‐Analog
Conversion
(DAC)
circuit
 
 (40
points)
 Assume
that
the
binary
input
voltages
are
0
V
for
“0”
and
5
V
for
“1”;
that
waveforms
 D0,
D1,
D2,
D3
obtained
during
time
intervals
T1
through
T8
are
fed
into
the
DA
 converter
circuit
with
R
=
50
kΩand
RF
=
5
kΩ.
 
 Show
a
sample
calculation
of
the
output
voltage
VOUT(T)
for
the
time
interval
T3
 © 2009 Alexander Ganago Page 1 of 1 EECS 314 Winter 2009 Homework set 9 Student’s name ___________________________ 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 Problem
5,
continued
 On
the
grid
below,
sketch
the
output
voltage
VOUT(T)
for
the
time
intervals
T1
 through
T8
 Carefully
label
the
vertical
axis
in
volts.
 © 2009 Alexander Ganago Page 2 of 2 EECS 314 Winter 2009 Homework set 9 Student’s name ___________________________ 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 Problem
6

 
 Logic
gates
and
Truth
tables
(20
points)
 The
Big
Picture

 Logic
gates
are
the
circuits
that
perform
logic
operations
on
signals
(input
voltages).

 The
input
signals
of
a
logic
gate
determine
its
output:
logic
gates
have
no
memory.
 For
the
given
inputs,
the
output
 depends
on
the
type
of
the
gate.
The
 relationship
between
the
inputs
and
 the
output
is
given
by
the
truth
table.

 The
Assignment
 In
each
part
of
this
problem,
consider
the
same
input
signals,
shown
on
the
sketch
as
 signal
1
and
signal
2.

 Assume
positive
logic,
that
it
high
voltage
 corresponds
to
logic
“1”
and
low
voltage
corresponds
 to
logic
“0”.
 In
each
part
of
the
problem,
assume
that
the
given
 input
signals
are
fed
into
an
unknown
logic
gate
 whose
output
is
shown
on
the
sketch.

 From
the
sketches,
determine
the
truth
table
of
each
 gate;
from
the
truth
table
determine
the
type
of
the
 logic
gate:
choose
from

 1. AND
 2. OR
 3. NAND
 4. NOR
 5. None
of
the
above.
 
 Input
1
 Input
2
 Output
 0
 1
 
 1
 1
 
 0
 0
 
 1
 0
 
 
 Logic
gate
 is

 ___________
 
 
 
 Continued
on
the
next
page
 © 2009 Alexander Ganago Page 1 of 2 EECS 314 Winter 2009 Homework set 9 Student’s name ___________________________ 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 Problem
6,
continued

 For
your
convenience,
the
input
waveforms
are
 repeated
here:
 
 
 
 
 
 
 
 Input
1
 Input
2
 Output
 0
 1
 
 1
 1
 
 0
 0
 
 1
 0
 
 
 
 Logic
gate
is
 
___________
 
 
 
 
 
 © 2009 Alexander Ganago Page 2 of 2 ...
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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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