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Computer System Applications: Design and Development
Laboratory Manual
Dr Mohammad Jahangir Ikram
Department of Computer Science
Lahore University of Management Sciences
Laboratory 3
Contents:
1. The A/D and D/A Conversion
1.1.
Introduction
1.2.
The Digital to Analog Conversion
1.2.1.
The Basic Conversion and Study of Quantization Error
1.2.2.
Waveform Generation
1.3.
The Analog to Digital Conversion
1.3.1.
Study of Basic Conversion
1.3.2.
Basic DSP Techniques
1.4.
Programming Project: FFT Analysis
Analog to Digital and Digital to Analog Conversion
What is digital?
Digital comes from the word digit, which in the world of computers means binary numbers. Computers on
their on can deal with digits like adding, subtracting, at very high speed. Our daily life, on the other hand, is not
really digital.
Shades of Gray: An Example
We not only see black and white but we also see shades between black and white, that is, gray. When you
look at a gray color, you probably never think about the percentage of black and white that has been mixed to make
that gray color, unless someone asks. As an example take a look at the following Diagram. This shows a gradient
(slow increase) of white color to black color. In between those two colors, it can said that there are infinite number
of shades of gray and it is not so easy to tell the exact ratio of black and white at, say, point A. It can be 1:1 or
1:1.1 or 1:1.234 or 1:1.234567 depending on how good you can measure.
White
Black
Point A
This kind of ambiguity is not good in the world of computers. So we need to ‘digitize’ the colors.
Now look at the following Diagram. It has four shades including black and white. Now for the following four
shades with equal steps from white
to black, we can exactly tell the ratio
of black and white. Either we can
tell that from the ratio table used to
make these shades (3:0, 2:1, 1:2,
0:3) or we can simply number them,
0 (00)
1 (01)
2 (10)
3 (11)
‘0’, ‘1’, ‘2’, ‘3’, with ‘0’ being the
whitest and ‘3’ being the blackest. A
binary number or count can also be associated to represent the shade as shown in the Diagram below. It is
important to know that the numbers associated with shades are mere representation for our reference. We could
have called them a,b,c,d or majha, sajha, goga, boota, or anything we like. A representation tells about the reality,
Lahore University of Management Sciences CS324
Dr Mohammad Jahangir Ikram
Experiment 3 Page 1
an ‘a’ (or ‘majha’) would then mean white and so on.
As we know from the knowledge of digital numbers, two binary numbers can only represent 4 different
shades including white and black. What if we had three binary digits to represent the shades? The new Diagram
will look like below.
This
shows
that
by
increasing
the
representation
numbers we can now show more
shades of gray. If someone ask
about shade 4 in a range 0-7, we
call exactly tell about the ratio of
black and white.
0 (000)
1
(001)
2 (010)
3
(011)
4
(100)
5
(101)
6
(110)
7
(111)
Using 4 binary numbers
(0001)
(0011) (0101) (0111) (1001) (1011) (1101) (1111)
to represent each shade as
1
5
9
13
11
3
15
7
shown below can further increase
the ‘resolution’ of shades between
black and white. Now a shade 5
on range 0 to 15 is perfectly
understood and there is no
0
4
2
6
8
10
12
14
ambiguity in it.
In binary
(0000)
(0100)
(0010)
(0110) (1000) (1010) (1100) (1110)
language, we can say a shade
0101 between 0000  1111 is
perfectly understood. Now it can
be said that the shades of gray has been ‘digitized’. A further increase in steps between shades will require more
numbers to represent a shade. An 8-bit binary number can represent 256 gray shades and a 24-bit binary number
can represent 16777216 or 16 million gray shades. Remember, the more are the steps in shades, more is the
resolution of the color and more we get closer to figure 1, that is, infinite number of shades, the real thing.
Another Example:
Another useful example is to represent a voltage. Say we
have a variable voltage source of 0-9 volts and we randomly set
the output voltage near the center. Now we use a ‘needle’
voltmeter to measure the voltage and suppose the meter gives the
following observation. What can you say about the reading, is it
4.95, 4.98, 4.94, 4.9394, 4.953467V? Yes, again there is some
ambiguity. Leave the voltmeter aside and let us think about
‘digitizing’ the voltage. If we divide the voltage between 0-9V in 0
four steps, we have 0V, 3V, 6V, 9V. Again we can choose some
other numbers (or letters) to represent these voltages. It can be:
I. ‘0’,’1’,’2’,’3’
II. ‘00’, ‘01’,’10’,’11’,
III. ‘a’,’b’,’c’,’d’,
IV. ‘majha’, ‘sajha’, ‘goga’, ‘boota’
4
Saad Jamal
Instruments
8
Volts
A ‘1’ or ‘01’ or ‘b’ or sajha would mean exactly 3.0000V. Since computers play with binary numbers, we choose
binary numbers to represent our voltage as shown in the table below.
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Voltage
Binary Representation
0V
00
3V
01
6V
10
9V
11
Dr Mohammad Jahangir Ikram
Experiment 3 Page 2
This means 00 represent 0V, 01 represent 3V and so on.
This can also be shown in a Diagram as below.
6V
(10)
3V
(01)
0V
(00)
9V
(11)
Now if we chose three binary numbers to represent a voltage, the table will be:
The above table is created by the fact that there are 8 steps between 0 to 9V, so each
step will 9/8 = 1.125V.
0V (000)
9V (101) Can you show this on the
following Diagram?
Similarly, using four binary numbers, we can build the following table (shown .
This time step size is 9/16 = 0.5625, even smaller than before.
Again write the representations on the above Diagram.
Voltage
Binary
Representation
of voltage
0.000V
000
1.125V
001
2.250V
010
3.375V
011
4.500V
100
6.750V
101
7.875
110
9.000V
111
When we use four
binary
numbers
to
(0000)
represent a voltage between 0-9V we get a step size
of 0.5625V or nearly ½ V.
Which is not very good. If we use 8-bits to
Binary
Voltage
represent a voltage between 0 – 9V, we get a step size of 9V/256 =
Representation of
0.03515625 or nearly 35mV. That means a ‘00000000’ would mean 0V and
voltage
‘11111111’ would mean 9V.
A ‘00000001’ would mean 0.03515625V
0.0000V
0000
precisely, and hence no ambiguity at all.
A ‘10110011’, which is 179 in
0.5625V
0001
decimal would represent 9V/256 X 179 = 6.29296875V to be precise.
9V
(1111)
0V
Review Questions:
1) 8 bit are used to represent voltage between 0-9, what voltage is
1001111? ___________
2) Repeat above for 11110000 ___________, 11101010 ________,
11001100 __________ .
3) If 12 bits are used to represent a voltage between 0-9V what will be the
step size?
4) If 12 bits are used to represent a voltage between 0-5V what will be the
step size?
0
Analog to
Digital
Converter
(ADC)
VIN (0- VMAX)
1
2
3
N-Bit Digital Output
representation.
(000 --- 0 = 0V and
111 … 1 = VMAX)
N
5)
If 12 bits are used to represent a voltage between 0-1V what will be the
step size?
Lahore University of Management Sciences CS324
Dr Mohammad Jahangir Ikram
1.1250V
0010
1.6875V
0011
2.2500V
0100
2.8125V
0101
3.3750V
0110
3.9375V
0111
4.5000V
1000
5.0625V
1001
6.1875V
1010
6.7500V
1011
7.3125V
1100
7.8570V
1101
8.4375V
1110
9.0000V
1111
Experiment 3 Page 3
Now all we need is a device that has analog (real) voltage input and an n-binary-number output as digital
representation. Such a device is called analog to digital converter (as shown in the diagram on the previous page).
The symbol of such a device is shown below:
Thousands of types of ADC are available in the market in the form of integrated circuits. As designer most people
do not need to study the actual mechanism of analog to digital conversion and they use these ICs as such
according the application notes available from the manufacturer. National Semiconductors is one of the companies
that makes ADCs and part search on national website: www.national.com can give you a lot of information on
ADCs along with application notes.
The Anatomy of ADCs
Almost all ADCs are made of one or more of the following components:
1)
2)
3)
4)
Comparator
Digital to Analog Converter (DAC)
A Digital Counter
An AND gate.
Voltage Comparator Circuit
Figure 7-4 shows the connections to a basic operational amplifier
comparator. The comparator has two input terminals, V1 and V2, and a single
output technical, V0. The voltage comparator compares two analog input
voltages and produces a digital output signal. The output is high if V1 is more
positive than V2; otherwise, the output is low (if V1 is less than V2). This circuit is
used in analog to-digital (A/D) converters to determine if an analog input signal
(V1) is greater than or less than a reference voltage (V2).
Digital-to-Analog
A digital-to-analog (D/A) converter is a circuit that produces an analog
Figure 7-4 Voltage
output voltage that is a function of a weighted parallel binary input. The output
comparator
voltage varies in steps, with the smallest possible step being controlled by the
least significant bit (LSB) of the input. For example, a four-bit D/A converter
would have 42, or 16, possible output
levels. The output might range from 0
to 15 mV, the difference between any
two adjacent levels being 1 mV. If the
input were stepped sequentially
through all 16 possible binary
combinations (i.e., 0 through 15), the
output voltage would look like a
staircase increasing in 1-mV steps
from 0 to 15 mV.
Figure 7-5 Operational amplifier R-2R resistive ladder D/A converter
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Dr Mohammad Jahangir Ikram
Experiment 3 Page 4
Most D/A converters use a weighted resistive ladder network in the form of ~n integrated circuit combined
with an operational amplifier, like that of Figure 7-5, to convert binary inputs to an equivalent analog output voltage.
The output voltage is incremented in steps of –1/2N times the voltage corresponding to a logic 1 of any of the,
binary inputs, where N is the number of bits. For example, if a 4-bit weighted resistor network is used, and the 4-bit
inputs are set at b0 = 1, b1 = 0, b2 = 1, and b3 = 0 (01012 = 510), then the output voltage of the D/A converter of
Figure 7-5 equals –5/16 times the logic 1 voltage of the logic family used. If TTL devices are used, then the logic 1
voltage is nominally 5 V. Thus this 4-bit D/A
converter has voltage increments of (–1/16)(5 V) = –
312.5 mV over the output range from 0 (all inputs at
logic 0) to-5 V (all inputs at logic 1). If the binary
inputs are 01012, as above, the output voltage is –
1.5625 V.
The Analog to Digital Converter
1. Staircase Ramp A/D Converter
Figure 7-8 A 4-bit staircase ramp A/D converter. (a) Block Diagram
(b) The binary counter stops when VR exceeds Vin
One of the simplest A/D converters uses the staircase
ramp technique illustrated in Figure 7-8. The principle is
similar to the ramp A/D converter discussed earlier in this
chapter, but the ramp generator is replaced in this case
with a D/A converter. The output of the D/A converter is
a 'staircase serving the same purpose as the analog ramp
in the ramp converter.
At the start of a conversion cycle, the
Counter is reset to zero; the output of the D/A
converter is also zero. At this point, the output of the
comparator is high, and the clock pulses go through
the gate to the counter. As the count increases, the
staircase waveform proceeds in increments towards
Vin. When the staircase voltage level exceeds Vin,
the output of the comparator goes low, and the
count stops. The count is converted in decimal,
term, and is used to update the display. The cycle
then repeats itself.
Successive Approximation A/D Converter
The two major drawbacks of the A/D
converters like dual-slope and staircase ramp A/D
converters are that (1) they are relatively slow and (2)
the conversion time is a function of the magnitude of
Vin. The successive approximation A/D converter
overcomes both these problems to a considerable
degree. It makes conversions in microseconds rather
than the several milliseconds required by the ramp,
dual-slope, staircase converters.
Although the block diagram for the successive
approximation A/D Converter in Fig. 7-9 looks very
much like that of a staircase ramp A/D converter, it
differs in the control logic section. Instead of allowing
the staircase to climb from zero through all sequential
steps up to Vin it first tries a step equivalent to the
most significant bit of the converter. If this step does
not exceed the value of Vin, it is retained in the storage
register. Otherwise, the storage register is set to zero.
Lahore University of Management Sciences CS324
Dr Mohammad Jahangir Ikram
Figure 7-9 A 4-bit successive approximation A/D converter
Experiment 3 Page 5
The next largest bit is then tried and so on until all bits have been tried in order of decreasing size. A significant
feature system is that it takes only N steps to produce an N-bit output, regardless of the magnitude of the input
signal.
The conversion time of the successive approximation converter is a constant and is given by N/f, where N
is the number of bits in the converter, and f is the clock frequency. Thus, a 10-bit converter with a 1-MHz clock
makes a conversion every 10s.
Flash Converter
As the name applies, this ADC is the fastest ADC but at the same time, it is very expansive. It uses
almost 2N operational amplifiers to give N-bit output. Further detail is beyond the scope of this course.
Experiment 3: Analog to Digital Conversion
In this experiment, we will study the working of
Integrated Circuit Analog to Digital Converter (ADC).
Pin Description of this IC is as follows:
CS (chip Select) is coming from the port decoder (big
AND gate). Note that the IC has internal output Latch as
well as a buffer.
RD is to read the output.
WR is start conversion
INTR is end of conversion
CLK In, CLK R are used for external clock generation.
Vin (+) and Vin(-) are pins where you apply external
ANALOG input.
DB0 to DB7 are Digital 8-bit output.
VREF/2 is used to set the input analog range. A 2.5V on
this pin will set range to 0 (output 00000000) to
+5V(output 111111112). Analog and Digital GND are
usually common.
Self Running Mode.
Usually, ADC are interfaced with computers though
Interrupts. If you are polling, then ADC are usually used
in Self-running mode. In self running mode Interrupt(end of conversion) output of the IC is tied with RD (start Conversion),
making the IC to continuously do conversions with out the intervention of a CPU. However, a kick-start switch is required at
power-up.
Following is the diagram used in this experiment.
Note that you have to press the kick start button ONLY
10K
+5V
once at power-up time.
Question 1: Why do we need kick start button?
Question 2: What is the step size of the ADC shown in
figure.
Analog Input
Digital Output
Kick Start
30pF
Digital Output
Vary the input voltage and measure it on the analog
multimeter. Read the corresponding digital output using
computer and fill the following table for a number of
readings.
0-5V Variable
Difference
2.5 Volt
Switch
Programming Assignment For LAB 3
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Dr Mohammad Jahangir Ikram
Experiment 3 Page 6
Write a software for digital voltmeter as explained in the LAB.
Laboratory
Fill the blanks for the following and get it signed by the TA
1. The maximum out put in binary is __________
2. The maximum analog input for that output is _________
3. What is digital output for 3.000 Volts input
4. What is step size in millivolts.___________
5. Using digital meter find the digital output values for closest following voltages:
a. 3.12 V _________
b. 2.5 V __________
c. 3.6 Volts ________
6. In all the above cases what is maximum difference between required output and the output that can be
achieved. ___________________
7. How can you relate results in 4 and 5 ____________________________
____________________________________________________________________
____________________________________________________________________
Lahore University of Management Sciences CS324
Dr Mohammad Jahangir Ikram
Experiment 3 Page 7
Computer System Applications: Design and Development
Laboratory Manual
Dr Mohammad Jahangir Ikram
Department of Computer Science
Lahore University of Management Sciences
Read Laboratory Notes carefully before you come to the class.
Laboratory 4
Digital to Analog Conversion
Connect the circuit as you will connect for the 8-bit DIP switch status
Repeat the above experiment part 1 in reverse order, that is for an digital input find a analog
output and make table as big as possible.
What is step size of the DAC_____________________
What is the minimum and maximum analog output.____________ , ___________
What would have been the step size if the DAC had 12-bit input _______________
Can you find the conversion time of DAC __________________
Fill the blanks for the following and get it signed by the TA
1. The maxim out put in Volts is __________
2. The maximum digital input for that input is _________
3. What is digital input for 3.000 Volts (Use digital meter)
4. What is step size in millivolts.___________
5. Using digital meter find the digital input values for closet following voltages:
6. 3.12 V _________
7. 2.25 V __________
8. 1.76 Volts ________
9. In all the above cases what is maximum difference between required output and the
output that can be achieved. ___________________
10. How can you relate results in 1.2.1.8 and 1.2.1.10 ____________________________
____________________________________________________________________
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Dr Mohammad Jahangir Ikram
Experiment 3 Page 8
____________________________________________________________________
1.2.1.1
For the plot of following sinusoidal waveform find approximate voltage level after each
mSec and write a software that will generate a ‘stepped’ simusoidal at the DAC
output.
4Volts
0 Volts
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Time in mSec
Dr Mohammad Jahangir Ikram
Experiment 3 Page 9