Bit patterns Analogue And Digital Flashcards
AQA Computer Science A-Level
4.5.6 Representing images
sound and other data
Intermediate Notes
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Specification:
4.5.6.1 Bit patterns
images
Describe how bit patterns may represent other forms of data
including
graphics and sound.
4.5.6.2 Analogue and digital:
Understand the difference between analogue and digital:
● data
● signals
4.5.6.3 Analogue/digital conversion:
Describe the principles of operation of:
● an analogue to digital converter (ADC)
● a digital to analogue converter (DAC)
Know that ADCs are used with analogue sensors.
Know that the most common use for a DAC is to convert a digital audio
signal to an analogue signal.
4.5.6.4 Bitmapped graphics:
Explain how bitmaps are represented.
Explain the following for bitmaps:
● resolution
● colour depth
● size in pixels
Calculate storage requirements for bitmapped images and be aware
that bitmap image files may also contain metadata.
Be familiar with typical metadata.
4.5.6.5 Vector graphics:
Explain how vector graphics represents images using lists of objects.
Give examples of typical properties of objects.
Use vector graphic primitives to create a simple vector graphic.
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4.5.6.6 Vector graphics versus bitmapped graphics:
Compare the vector graphics approach with the bitmapped graphics
approach and understand the advantages and disadvantages of each.
Be aware of appropriate uses of each approach.
4.5.6.7 Digital representation of sound:
Describe the digital representation of sound in terms of:
● sample resolution
● sampling rate and the Nyquist theorem
Calculate sound sample sizes in bytes.
4.5.6.8 Musical Instrument Digital Interface (MIDI):
Describe the purpose of MIDI and the use of event messages in MIDI.
Describe the advantages of using MIDI files for representing music.
4.5.6.9 Data compression:
Know why images and sound files are often compressed and that other
files
such as text files
Understand the difference between lossless and lossy compression and
explain the advantages and disadvantages of each.
Explain the principles behind the following techniques for lossless
compression:
● run length encoding (RLE)
● dictionary-based methods
4.5.6.10 Encryption:
Understand what is meant by encryption and be able to define it.
Be familiar with Caesar cipher and be able to apply it to encrypt a
plaintext message and decrypt a ciphertext. Be able to explain why it is easily
cracked.
Be familiar with Vernam cipher or one-time pad and be able to apply it
to encrypt a plaintext message and decrypt a ciphertext. Explain why Vernam
cipher is considered as a cypher with perfect security.
Compare Vernam cipher with ciphers that depend on computational
security.
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Bit patterns
images
So far
we’ve only seen bit patterns used to represent numbers. However
use bit patterns to represent all other forms of data
including pictures and sound.
Analogue and digital
Analogue data has no limits to the values that it can take. In contrast
digital data can only
take particular values.
Analogue and digital signals vary in a similar way. An analogue signal can take any values
and can change as much as required whereas a digital signal must always take one of a
specified range of values and can only change value at specified intervals.
Analogue signal
Digital signal
Analogue/digital conversion
Digital to analogue conversion
When converting from digital to analogue
a device called a digital to analogue converter
(or DAC for short) is used. The device reads a bit pattern representing an analogue signal
and outputs an analogue electrical current.
Analogue to digital conversion
When a computer needs to make use of analogue sensors
they use an analogue to digital
converter (ADC for short) to convert the analogue signal to a digital bit pattern. The device
works by taking a reading of an analogue signal at regular intervals and recording the
value in a process called sampling.
Samples are taken at a specific frequency
which determines the number of samples taken
per second. This is usually a high number.
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Once the value of the analogue signal has been recorded
it can be stored digitally as a bit
pattern.
Bitmapped graphics
Computers represent images in two different ways
one of which is by using bitmap
graphics. In bitmap graphics
an image is broken down into pixels
binary value assigned to it.
The resolution of an image refers to the number of pixels in an image
for example
image below could be said to have a resolution of 5 × 5 pixels.
The value assigned to a pixel determines the colour of the pixel. The example below
shows the binary representation of a simple bitmap image in which a 1 represents a black
pixel and a 0 represents a white pixel.
1 0 0 0 1
1 1 0 1 1
1 0 1 0 1
1 0 0 0 1
1 0 0 0 1
The number of bits assigned to a pixel in an image is called its colour depth. In the
example above
each pixel has been assigned one bit
represented.
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00 11 11 11 11 11 00
11 11 11 11 11 11 11
11 00 01 11 00 01 11
11 00 00 11 00 00 11
11 11 11 11 11 11 11
11 11 10 10 10 11 11
00 11 11 11 11 11 00
In order to calculate the storage required to represent a bitmap image
multiply the number
of pixels (width × height) by the bit depth.
The picture of the face has 7 × 7 = 49 pixels
each of which is assigned two bits
requires 98 bits to be represented.
7 × 7 × 2 = 98 bits
This method of calculating the storage requirements for bitmapped images produces a
minimum value. This is because bitmap image files may also contain metadata
typical
examples of which include the image’s width
height
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Vector graphics
Vector graphics represent images using objects and shapes such as rectangles
circles
and lines. The properties (such as fill colour
fill style and dimensions) of each geometric
object or shape in the image are stored in a list.
shape
properties
rectangle
fill-colour: green
fill-style: solid
height: 2
width: 10
start-position: (0
0)
square
fill-colour: yellow
fill-style: vignette
width: 6
start-position: (4
2)
triangle
fill-colour: grey
fill-style: solid
width: 7
start-position: (3
8)
Vector graphics versus bitmapped graphics
Because vector graphics use shapes rather than pixels
they can be enlarged without
losing quality. Enlarging a bitmap image results in a blurry or even pixelated image
whereas enlarging a vector graphic results in no loss of clarity.
Vector graphics frequently use less storage space than bitmapped graphics
as
information is stored for each shape
rather than for every single pixel in an image.
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Digital representation of sound
Computers represent sound as a sequence of samples
each of which takes a digital
value. The number of samples per second is called the sampling rate.
Analogue signal sampled
Samples used to recreate signal
digitally
The number of bits allocated to each sample is referred to as the sample resolution.
Higher sample resolutions result in greater audio quality but also increased file size.
The size of a sound sample can be calculated by multiplying together the duration of the
sample in seconds
the sampling rate in Hertz and the sample resolution.
For example
a 45 second long audio file sampled at 500 Hz with a sample resolution of 16
bits would require 45000 bytes of storage.
45 × 500 × 16 = 360000 bits
360000 ÷ 8 = 45000 bytes
The Nyquist Theorem
The Nyquist theorem states that the sampling rate of a digital audio file must be at least
twice the frequency of the sound. If the sampling rate is below this
the sound may not be
accurately represented.
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Musical Instrument Digital Interface (MIDI)
Musical instrument digital interface
or MIDI
which can be connected to computers. MIDI stores sound as a series of event messages
each of which represents an event in a piece of music. These can be thought of as a
series of instructions which could be used to recreate a piece of music.
Event messages could contain information such as:
● The duration of a note
● The instrument with which a note is played
● How loud a note is (its volume)
There are numerous advantages to using MIDI over a sampled recording of a piece of
music. Using MIDI allows easy manipulation of music without loss of quality. The
instruments on which notes sound can be changed
notes can be changed and the
duration of notes can be altered.
Furthermore
MIDI files are often smaller in size than sampled audio files.
However
MIDI can’t be used for storing speech and sometimes results in a less realistic
sound than sampled recordings.
Data compression
FIles are compressed in order to reduce their size. Smaller files can be transferred faster
between storage devices.
Images are often compressed
but sound files and text files can also be compressed.
There are two categories of compression
lossy and lossless.
Lossy compression
When using lossy compression
some information is lost in the process of reducing the
file’s size. This could be reducing the resolution of an image or lowering the sample
resolution of an audio file.
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Lossless compression
In contrast to lossy compression
there is no loss of information when using lossless
compression. The size of a file can be reduced without decreasing its quality.
Two methods of lossless compression are run length encoding and dictionary-based
methods.
Run length encoding (RLE)
Run length encoding (RLE for short) reduces the size of a file by removing repeated
information and replacing it with one occurance of the repeated information followed by the
number of times it is to be repeated.
BLUE
5
BLUE
2 PURPLE
3
BLUE
2 YELLOW
3
BLUE
2 PURPLE
3
BLUE
2 YELLOW
3
Using RLE to replace repeated pixels with one pixel colour and a number or repetitions
reduces the storage space required to represent the image.
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Dictionary-based methods
When a file is compressed with a dictionary-based method
a dictionary containing
repeated data is appended to the file.
For the picture above
the dictionary on the left could be used.
= 1
1
2
= 2
3
2
= 3
3
Using the dictionary
the file could be represented using just the data 12323
as shown on
the right.
This method results is a significant reduction in size
but don’t forget that the dictionary
used to compress the data has to be present in the file in order for the image to be
reproduced. This will increase the size of the file.
Lossy Compression
Lossless Compression
Some information is lost in the
compression process
No loss of information
Quality of file is reduced
No loss of quality
Encryption
Encryption is the process of scrambling data so that it cannot be understood if intercepted
in order to keep it secure during transmission. Unencrypted information is referred to as
plaintext and encrypted information is called ciphertext. A cipher is a type of encryption
method.
In order to decrypt ciphertext
you must know the encryption method used and the key
used to encrypt the information.
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Caesar ciphers
Caesar ciphers encrypt information by replacing characters. One character is always
replaced by the same character. There are two types of Caesar cipher that you need to be
aware of. Shift ciphers and substitution ciphers.
Shift ciphers
When encrypting using a shift cipher
all of the letters in the alphabet are shifted by the
same amount. The amount by which characters are shifted forms the key.
Plaintext
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
X Y Z A B C D E F G H I J K L M N O P Q R S T U V W
Ciphertext
The example above uses a shift of three characters
so the key is three. Using the key
three
the plaintext “BAT
” could be encrypted as the ciphertext “YXQ
”.
Substitution ciphers
Substitution ciphers are a type of Caesar cipher in which letters are randomly replaced.
Plaintext
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
F J E D M K B I C H L S A T U R V W G Y Q N P Z X O
Ciphertext
Using the cipher in the example
the plaintext “DOG
” would be encrypted as “DUB
”.
Caesar ciphers can be easily cracked. For example
the most frequently occurring letter in
an encrypted message is likely to be an E
.
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Vernam ciphers
The Vernam cipher is an example of a one-time pad cipher. This means that each key
should only ever be used once. Additionally
the Vernam cipher requires the key to be
random and at least as long as the plaintext that is to be encrypted.
The Vernam cipher works by:
- Aligning the characters of the plaintext and the key
- Converting each character to binary (using an
information coding system)
- Applying a logical XOR operation to the two bit
patterns
- Converting the result back to a character
Example
encrypting:
H
I
1001000
1001001
u
r
Key binary
1110101
1110010
Plaintext binary
XOR key binary
111101
111011
=
;
Plaintext
Plaintext binary
Key
Ciphertext
In the example above
each of the characters in the plaintext and the key are converted to
binary
then XORed before being converted back to characters.
As the example shows
the plaintext HIis encrypted by a Vernam cipher with the key ur
as the ciphertext =;
.
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Example
decrypting:
When decrypting using a Vernam cipher
the key that was used to encrypt the plaintext is
used again.
=
;
111101
111011
u
r
Key binary
1110101
1110010
Ciphertext binary
XOR key binary
1001000
1001001
H
I
Ciphertext
Ciphertext binary
Key
Plaintext
The Vernam cipher is the only cipher mathematically proven to be completely secure.
Computational security
All ciphers other than the Vernam cipher are
in theory
reasonable timeframe given current computing power. Ciphers that use this form of
security are said to rely on computational security.
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