Topic 14:
Digital
Technology
Binary numbers
• In ordinary arithmetic, we use the decimal system to represent number. Digits from 0 to 9 are used in this system.
•In the binary system numbers are represented using only two digits: 0 and 1.
Consider the decimal number 5037.
thousands hundreds tens units
Digits:
In fact, we could write this number in terms of powers of 10.
Binary numbers
• So, the digits of a decimal number are just the coefficients of various powers of 10. These coefficients can be digits from 0 to 9.
• The same idea applies to binary numbers. But instead of using powers of ten we will be using powers of 2. And the coefficients are the digits 0 or 1 instead the digits from 0 to 9. • To express a decimal number in the binary system, we must write that number as a sum of powers of two with coefficients that are either 0 or 1.
Example: 5 = 1 x 22 + 0 x 21 + 1 x 20
So, the binary representation of 5 will be
Binary numbers
12 = 1 x 23 + 1 x 22 + 0 x 21 + 0 x 20
122 = 1100
13 = 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20
132 = 1101
14 = 1 x 23 + 1 x 22 + 1 x 21 + 0 x 20
Binary numbers
• With four-bit words (that is, four digits) we can only represent 16 number (from 0 to 15).
• For each of the four digits we have two choices: 0 or 1. • The total number of choices is then 2 x 2 x 2 x 2 = 16. • To represent larger number we have to increase the
number of bits in the binary representation of the number.
Example:
43 = 1 x 25 + 0 x 24 +1 x 23 + 0 x 22 + 1 x 21 + 1 x 20
Binary numbers
210 = 1024
29 = 512
28 = 256
27 = 128
26 = 64
25 = 32
24 = 16
23 = 8
22 = 4
21 = 2
20 = 1
753 = 512 + 128 + 64 + 32 + 16 + 1
So,
7532 = 1011110001
Binary numbers
• Given a number in binary form, we call the first non-zero digit the most significant bit (MSB) and the last digit (the digit the number ends with) the least significant bit (LSB).
For example, 01110 has 1 as it MSB and 0 as it LSB
Solve problems involving the
conversion between binary numbers
and decimal numbers.
Students should be aware of the term bit. An awareness of the least-significant bit (LSB)
and most-significant bit (MSB) is required. Problems will be limited to a maximum of five
Sample Problem
The binary equivalent of the number 12 is A. 1010.
How microphones work
1. Sound waves carry energy toward the microphone.
2. The diaphragm moves back and forth when sound waves hit it. 3. The coil, attached to the diaphragm, moves back and forth as well. 4. The permanent magnet produces a magnetic field that cuts through
the coil. As the coil moves back and forth through the magnetic field, an electric current flows through it.
Analog and digital signals
• When one speaks into a microphone, a voltage is created in the microphone.
• The voltage is proportional to the actual physical movement of the diaphragm of the microphone.
• A large voltage is created when the diaphragm moves fast, and a small voltage when it moves slowly.
• The voltage signal so generated varies continuously
between two extreme values.
Analog and digital signals
Analog signals are continuous signals, varying between two extreme values in a way that is
Analog and digital signals
Analog and digital signals
•Consider a potential divider circuit.
•The emf of the battery is 8V which means that the
reading of the voltmeter can be any number between 0 and 8, depending on where the lead connects to the variable resistor R.
Analog and digital signals
• Imagine that the point of contact is moved from the bottom end of the resistor to the top at constant
speed and assume that this is done in 4 ms.
Analog and digital signals
• This Analog signal must be sampled, which means it must be measured.
• This is done at regular intervals of time.
• The number of times per second the signal is sampled is called the sampling rate or sampling frequency.
• Sampling the signal means that we observe it for very short intervals of time, wait, and then sample it again.
• Thus we do not, in general, know how the signal behaves in between the instants of time when it is sampled.
• Typically, for audio signals, a sampling rate of 8000 times per second is used.
Analog and digital signals
• The actual duration of one sample is very short (1.0 s or even less).
• This is why sampled signals are represented by vertical lines of practically zero width.
• When a Analog signal is converted into a digital signal, that is, when we convert a voltage into binary number, we must decide how big will our bit word will be.
• If we use two-bit words, the we will have at most 22 = 4
words (00, 01, 10, 11).
Analog and digital signals
• The range of the original voltage is divided into 4 levels (if we use 2-bit words) and each level will be assigned a 2-bit word.
• In each level there is a lower boundary and an upper boundary
• In this case, there was a loss of information during the digitization of the original data.
Analog and digital signals
• The process of dividing the range of the Analog signal into a set of levels is called quantization and the levels themselves are called quantization levels.
• The number of quantization levels is determined by the length of the word to be used, that is, by the number of bits used. With n bits the number of quantization levels is
2n.
• This gives rise to the notion of quantization error.
Suppose that the Analog signal varies from a minimum value of m and a maximum value of M and we use n-bit words to digitize it.
• The number of quantization levels is 2n, and so at each
Analog and digital signals
• The quantity
n
m
M
q
2
is known as the quantization error of the digitization process.
• Two Analog signals that differ less than the quantization error are assigned the same binary number.
Compact disks
• The CD is a disk of diameter 12cm. The Analog signal is converted into a digital signal (‘0’s and ‘1’s) and then
imprinted on the CD.
•A compact disk (CD) is a device on which information can be stored in digital form and the retrieved.
•This is done by doing marks called pits on the CD. The parts of the CD without pits are called
lands.
•The edge of a pit corresponds to binary ‘1’.
Compact disks
1600 nm 500 nm 830 - 3560 nm land
pit
Compact disks
• The bottom part of the disk (the side that is actually being read) is covered with optically transparent material (polycarbonate).
•A CD is read using a laser beam. The laser cannot have zero width. •So when the beam is incident near the edge of a pit, a few rays will be reflected off the pit and the rest will be reflected of the land. •This causes destructive
How A Compact Disc Works
Hyperlink
Compact disks
Reading a CD
As the disk rotates, the laser reflects off the sequence of bumps and lower areas into a photodector
– The photodector converts the fluctuating reflected light
intensity into an electrical string of zeros and ones
The pit depth is made equal to one-quarter of the
wavelength of the light
λ/4 depth, so that the wave travels λ/2 further, and destructively
interferes
When the laser beam hits a rising or falling bump edge, part of the beam reflects from the top of the bump and part from
the lower adjacent area
Compact disks
• The wavelength of the laser light used is about 780nm in air. • The refractive index of the polycarbonate material is 1.55,
which means that the wavelength of light in the polycarbonate is:
•The pit depth for destructive interference to occur must be:
nm
n
air503
55
.
1
780
nm
d
126
4
503
4
Example Problem
The depth of a “pit“ on a CD is 150 nm. The wavelength of the laser used to read the
information on the CD must be
Compact disks
• The laser source moves outwards and so follows the spiral of the pits and lands as the disk rotates.
• Because the circumference is getting longer as we move outwards, the rate of rotation of the disk is
reduced, so that the laser can sample the disk at the same rate.
DVDs
• Because the pit length is shorter than on a CD, more data can be stored along the spiral.
• Also, data can be stored on both sides of the disk or in a double layer on the same side.
• Overall, this results in more than seven times the storage capacity compared to that of a CD.
Blu-Ray
Blue laser formats have a shorter wavelength (405 nm) then CD and DVD formats which use a red laser (650 nm - DVD read wavelength). Blue ray’s blue laser beam focuses much tighter then a red laser. This allows for much tighter alignment of pits (areas of darker contrast on a recordable disc). This tighter collection of pits allows for greater storage, 27GB with the first
LPs
• In Edison’s original sound recording in 1877, sound was incident on a diaphragm, which therefore began to vibrate. • A needle attached to the diaphragm then made marks on
a rotating tinfoil-covered cylinder.
• The ‘marks’ were a direct, mechanical copy of the actual audio signal.
• During playback, the needle retraces the pattern scratched on the cylinder surface and now makes the diaphragm
LPs
• In the later vinyl LPs (Long-Play) the principle of recording is essentially the same.
• But instead of a rotating cylinder, a flat rotating disk is used.
• During playback the signal is amplified electrically and fed into a loudspeaker, rather than making a diaphragm
vibrate.
Cassettes
• These devices use magnetic
recording to store data in an Analog form.
• They are called sequential devices
as you must wind the cassette to get to the wanted song and this takes some time.
• The recording takes place on the
ribbon of the cassette, which is made out of a strong plastic coated in ferric oxide, a ferromagnetic material.
Cassettes
• This current produces its own varying magnetic field.
• When the cassette is exposed to this magnetic field, a ‘copy’ of this magnetic field is created on the tape.
• During playback, the magnetic field stored on the magnetic tape will induce an electric current in a coil, which can be converted into an audio signal playing the music that was recorded.
• The advantages have been its low price and availability. Also, the tape could be erased and new material recorded
• The disadvantages refer to the sequential nature of the
device, its limited storage capacity and being sensitive to high temperatures and easily damaged.
Floppy disks
• The floppy disk, like the cassette, uses magnetic recording.
• The original was invented in the mid-1960s at IBM as a way of inputting data into a
computer as well as storing computer data. • Its name comes from the flexible nature of
the disk.
• Data was stored magnetically but in
concentric rings, which had the advantage that one could access data on an outer ring without having to go sequentially through the intermediate data as on a cassette. • This provided a direct access storage
Floppy disks
Floppy Disk Drives
• Qume D/T 8, 8 inch drive, 1.2 MB. This drive was made in 1980.
• Tandon TM 100-2A with IBM logo, 5 ¼ inch drive, 360 KB. This drive was made in 1983.
Hard disks
• Hard disks started being used only in computers.
• Nowadays, they are used in digital cameras, digital video recorders, mobile phones and other devices.
• They store data in large quantities.
• The device itself consists of a number of disks made of aluminium or glass arranged on a spindle.
Hard disks
• The surface may be thought to be divided into a very large number of tiny regions and each such region is the seat of a ‘0’ or a ‘1’ of
digitized data.
• The growth of hard disk capacity has been exponential. Early PCs had hard disks with a capacity of just a few MB. Today’s PCs have a hard disk capacity of hundreds of GB.
• The data is stored in sectors and tracks. Tracks are concentric rings and a sector is a part of the same track.
Advantages of digital storage
• The capacity for data storage is huge in digital devices.
• The access to particular stored data is fast. • The retrieval of data is fast.
• The storage is reliable.
• The stored data can be copied or erased easily. • The stored data can be encrypted.
• The data can be processed and manipulated by a computer.
Disadvantages of digital storage
• On the negative side, whereas an Analog storage system, such as ordinary photographic film,
