Ch26 Coding Systems

Sam Sully
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Sam Sully
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To help you revise coding systems/data representation.

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Ch26 Coding Systems
1 Character Set
1.1 A table which maps each character with a unique binary number.
1.2 ASCII
1.2.1 American Standard Code for Information Interchange
1.2.2 7 bits, so holds 128 characters.
1.2.3 More recently extended ASCII was released, 8 bits, 256 characters.
1.2.4 Only contains basic English characters and punctuation.
1.2.5 Not enough: advent of World Wide Web created need for universal system.
1.3 Unicode
1.3.1 Was brought in to replace Unicode and include most characters from across the world.
1.3.1.1 Note: this includes Emojis!
1.3.1.2 Includes the characters for over 20 countries.
1.3.2 16 bit so can code for around 6.5 thousand characters.
1.3.3 Constantly updated and maintained by the Unicode Consortium.
2 Error Checking
2.1 Parity Bit
2.1.1 Where an additional bit is added to the end of a binary number to show whether there are an even or an odd number of 1 digits.
2.1.2 Unreliable as if an even number of bits flip or the parity bit flips, it doesn't detect the error.
2.2 Majority Voting
2.2.1 Data is sent multiple (typically 3) times and if there is a discrepancy, the computer goes with the majority.
2.2.2 Very reliable and can correct data without retransmitting, however, uses a lot of bandwidth.
2.3 Check Digit
2.3.1 An additional digit is added to the end of a number which is derived from the number.
2.3.2 A simple method is by simply adding up all the digits, and adding up the digits on the sum, repeat this until you are left with a single number.
2.3.2.1 This is unreliable as if the order changes, the check digit remains the same.
2.3.3 A more advanced method would multiply each number by a weight, so as to ensure that order is needed. An example of this is the modulo-11 method.
3 Graphics
3.1 Bit Maps
3.1.1 A bit map graphic is a 2D array of pixels.
3.1.2 Each pixel holds a colour value, stored as a binary number, many thousands of these pixels typically make up an image.
3.1.3 A problem with bit maps is that quality degrades when you zoom in, additionally they take up a large amount of space.
3.1.4 Each pixel will have a colour depth, which is the number of bits allocated to represent the colour of a pixel, the higher the colour depth, the more colours that can be expressed.
3.2 Vector Graphics
3.2.1 A vector graphic is an image generated from a set of instructions and mathematical formulae. This generates the image consisting of geometric shapes, relative to a point of origin.
3.2.2 These are not suitable for photos as they simplify things significantly, however, they are good for diagrams and CAD/CAM images.
3.2.3 A vector graphic typically takes up little space and can be easily scaled up without losing quality.
4 Audio
4.1 Audio is converted to digital data by sampling the sound wave many times per second.
4.1.1 The higher the number of samples per second (measured in Hz), the higher the quality of the sound and the truer it is to the original.
4.1.1.1 The computer then synthesises a wave by extrapolating the data sampled, this is usually indistinguishable from the original for a human ear.
4.2 Nyquist's Theorem states that to faithfully recreate sound, you must record at least twice the highest frequency.
4.3 Humans hear 20Hz to 20kHz.
4.4 The resolution of sound is the number of bits allocated to each sample, hence, the more bits allocated, the more pressure levels each sample can represent.
5 Compression
5.1 Lossy compression
5.1.1 Some data is discard, to reduce file size, however, the new file is usually indistinguishable from the original.
5.1.2 An example would be replacing the hundreds of different shades of blue in an image of the sky, with just a few shades. A human would probably not notice the difference.
5.1.3 JPEG files use this.
5.1.4 It can be useful when transmitting images across the internet, as it reduces the bandwidth significantly. This is especially important for people on slow connections.
5.2 Lossless compression
5.2.1 Compression of data in such a way that the original data can be reacquired in it's totality, after decompressing. i.e. no data is discarded.
5.2.2 Examples would be run length encoding, where for example, if in an image, there are many pixels of the same colour, the computer just stores this as x*"blue" pixels. Rather than storing "blue pixel", "blue pixel"... This doesn't lose accuracy, it just encodes repeated data more simply. Another example is dictionary-based encoding, where commonly occurring strings in a text file are coded for in a simpler way, perhaps by assigning some token. A simple way to understand this could be replacing every "and" with an "&" this takes up 67% less space than writing "and". Again, no loss of accuracy as the original data can be easily reacquired.
5.2.2.1 Dictionary based encoding can be used on binary data also, if it is considered as a string of 1s and 0s.
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