Student of the Week
DEVIL PHYSICS
THE BADDEST CLASS ON CAMPUS
IB PHYSICS
TSOKOS LESSON 8-1
ANALOGUE AND DIGITAL
SIGNALS
Assessment Statements
IB Topic 14.1., Analogue and Digital Signals
14.1.1. Solve problems involving the conversion
between binary numbers and decimal
numbers.
14.1.2. Describe different means of storage of
information in both analogue and digital
forms.
14.1.3. Explain how interference of light is used
to recover information stored on a CD.
Assessment Statements
IB Topic 14.1., Analogue and Digital Signals
14.1.4. Calculate an appropriate depth for a pit
from the wavelength of the laser light.
14.1.5. Solve problems on CDs and DVDs
related to data storage capacity.
14.1.6. Discuss the advantage of the storage of
information in digital rather than
analogue form.
Objectives
 Convert decimal numbers into binary




numbers and vice versa
Understand the difference between an
analogue signal and a digital signal
Convert an analogue signal into a digital
signal
Outline the structure of a compact disc
Appreciate the role of interference in reading
a CD
Objectives
 Calculate pit depths in terms of the
wavelength of light used
 Outline the basic structure of various storage
devices
 Outline the advantages of digital storage
Introductory Video – Digital TV
Introductory Video – Digital
Telephones
Binary Numbers
 In the decimal, or base 10, system we use the
digits 1-9 and place value based on powers of
10
5037  5 x10
3
  0 x10   3 x10   7 x10 
2
1
0
Binary Numbers
 In the binary, or base 2, system we use the
digits 0-1 and place value based on powers of
2

  0 x 2   1 x 2   101
19  1 x 2   0 x 2   0 x 2   1 x 2   1 x 2   10011
10101  1 x 2   0 x 2   1 x 2   0 x 2   1 x 2 
5  1x 2
2
1
0
2
4
3
4
2
3
2
10101
2
 16  0  4  0  1  21
1
2
0
1
0
2
Binary Numbers
 In the binary system, each place value is
called a bit
 10101 has five digits so it is a 5-bit word
 The number of values is limited by the
number of bits
 5-bit numbers have 25 values = 32 values
 A 16-bit word has 65,536 possible values
 A 32-bit word has 4,294,967,296 possible values
 Newer systems are 64-bit which has a whole
bunch of values
Binary Numbers
 In a binary number, the first non-zero digit
(left side) is the most significant bit (MSB)
 The last digit is the least significant bit (LSB)
 In the binary number 011101,
 The first 1 (24) is the most significant bit and
 The last 0 (20) is the least significant bit
Analogue Signal
 Analogue signals are
continuous signals,
varying between two
Extreme values in a way that is proportional to
the physical mechanism that created the signal.
 A mercury thermometer gives a continuous
measurement of temperature
 A microphone produces a continuous voltage
signal based on the vibrations of a diaphragm
Digital Signal
 Digital signals are coded
forms of a signal that takes
discrete values of 0 or 1 only.
 The LabQuest with a temperature probe is
programmed to take x number of samples per
second and is idle between measurements
Converting an Analogue Signal
to Digital Signal
 Consider an analog
signal that increases at
a constant rate (linear
relationship)
Converting an Analogue Signal
to Digital Signal
 If we then sample it at
consistent intervals we
obtain
Converting an Analogue Signal
to Digital Signal
 We take a reading at
certain intervals and
don’t ‘know’ what
happens in between
 The number of
samples per second is
the sampling rate or
sampling frequency
Converting an Analogue Signal
to Digital Signal
 A typical sampling rate
for audio signals is
8000 times per second
or once every 125 μs
 This graph is called a
pulse amplitude
modulated signal
 The time to take a
sample is very short
compared to interval
Converting an Analogue Signal
to Digital Signal
 We now convert the
signal sampling into a
binary code using 2-bit
words
 22 means we can have
4 distinct values
 In a sense, this is like
rounding the signal to
significant parts
Converting an Analogue Signal
to Digital Signal
 We can decrease the
amount of ‘lost’
information by using
3-bit words
 23 means we can have
8 distinct values
 Increased intervals /
values means
increased fidelity
Converting an Analogue Signal
to Digital Signal
 Division of values into
specific ranges is
called quantization
and the levels are
quantization levels
Converting an Analogue Signal
to Digital Signal
 This gives rise to
quantization error
q
Max  Min
2
n
 For the 2-bit data the
error is 2V
 For the 3-bit data the
error is 1V
Compact Disks
Compact Disks Are The Pits
 Analogue data is
converted to
digital if required
 Digital data is then
imprinted on the
CD by a series of
marks called pits
 The edge of a pit
corresponds to a
binary ‘1’
Compact Disks Are The Pits
 The ‘unpitted’ part
is called a land.
 A series of pits are
made along a path
that spirals from
the center outward
Compact Disks Are The Pits
 Distance between
paths = 1600 nm
 Width of a pit = 500
nm
(comparable to the
λ of green light)
 Pit length = 830 nm
to 3560 nm
 Pit depth = 125 nm
Compact Disks Are The Pits
Compact Disks Are The Pits
 Bottom of the disk is coated with transparent
material
 CD’s are read by a laser from the bottom
Compact Disks Are The Pits
Compact
Disks Are
The Pits
 Because the laser beam can’t have zero width, as
the beam approaches a pit, some of the beam will
be reflected off the land, some off the pit
Compact
Disks Are
The Pits
 This produces interference
 The light reflected off a land travels 2d more than
light reflected off a pit
Compact
Disks Are
The Pits
 The light reflected off a land travels 2d more than
light reflected off a pit
 If we choose 2d to be half a wavelength
d 

4
Compact
Disks Are
The Pits
 If we choose 2d to be half a wavelength,
the interference between the two
reflections will be destructive and the
reflected light will have zero intensity
d 

4
Compact
Disks Are
The Pits
 
 air
n
 Wavelength of laser light is
about 780 nm
 Index of refraction is 1.55

780
1 . 55
 503 nm
Compact
Disks Are
The Pits
d 

4
 Pit depth is then about 126
nm

503
4
 126 nm
Other Storage Devices
 DVDs
 LPs
 Cassettes
 Floppy Discs
 Hard Discs
 Read Pages 459-461 to know the advantages
and disadvantages of each of these (this is
eerily like the advantages and disadvantages
of different energy sources)
Advantages of Digital Storage
 Read Page 461
 Know advantages and disadvantages
Summary
 Can you convert decimal numbers into binary




numbers and vice versa?
Do you understand the difference between
an analogue signal and a digital signal?
Can you convert an analogue signal into a
digital signal?
Can you outline the structure of a compact
disc?
Do you appreciate the role of interference in
reading a CD?
Summary
 Can you calculate pit depths in terms of the
wavelength of light used?
 Can you outline the basic structure of various
storage devices?
 Can you outline the advantages of digital
storage?
QUESTIONS?
Homework
#1-19