55 lines
2.1 KiB
Markdown
55 lines
2.1 KiB
Markdown
---
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tags:
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- binary
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---
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# Binary encoding
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We know that everything going on in a computer is the manipulation of binary
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digits. Thus all data must ultimately reduce to binary numbers manipulated
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through logic circuits.
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_Encoding_ is the process of establishing a correspondence between sets of
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binary numbers and sets of symbols that are representative of a given type of
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data. For certain fundamental data types, for example alphanumeric characters
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and colours, there are agreed standards of encoding such that, for example, that
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`111111` (binary) and `3F` (hex) always corresponds to the character `?`. The
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reverse is obviously _decoding_: deriving the data/ symbol from the binary
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format.
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> An encoding system maps each symbol to a unique sequence of bits. A computer
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> then interprets that sequence of bits and displays the apppropriate symbol to
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> the user.
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The length of the binary number (sometimes called the _word length_)
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corresponding to 8-bit, 16-bit, 32-bit etc. that is used to represent a given
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data set is determined by the number of variations that you require to capture
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the entire range of the dataset:
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> An $n$-bit binary system can encode $2^n$ different things
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For example, say we know that there are 18 levels to a computer game. To encode
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a reference for each level we would need a binary number that is capable of at
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least 18 total variations. In this instance a 32-bit ($2^{5}$ ) number would be
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best because the next smallest (16-bit) would not be sufficient. Our levels
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would have representations as follows:
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```
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00001 (1)
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00010 (2)
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00011 (3)
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00100 (4)
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...
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```
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## Related points
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Think about when you open a file format in a text editor that cannot decode it.
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For example trying to open a Word document in VSCode. The mangled letters it
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displays is the encoded binary data. When you open the file in Word, the
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decoding is applied and it resembles what you would expect.
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When we save a file, the different file extensions denote different formats and
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these are encoding formats. For example if you save an image file as `.png`
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rather than `.jpg`, you are applying a different encoding algorithm to the data
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that compresses the raw binary data in a different way.
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