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