I understand that data on computers can be compressed (I see it all the time with zip files and jpegs) but I was wondering just how compression works. Thinking it through, if you data is represented by 1s and 0s then it can be corresponded 1 to 1 with a binary number (albeit a large one). The idea behind compression is that some smaller number can represent the same data, but how is this possible since that new number must represent something else? I suppose if you know in advance that this number is a compressed version of another number than you can interpret it differently? Are there any relatively simple compression algorithms?
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If the algorithm was "simple" it probably wouldn't compress very well. If it helps you understand better, many compression algorithms actually can end up making a chunk of data larger if it's not suited for the task (notice how sound files don't compress very well at all with ZIP compression).
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