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Computers store data in binary digits - ones and zeroes. It is mainly here that hexadecimal is used, as a shortcut for binary; each hexadecimal digit corresponds to four binary digits.

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Computers work in powers of 2 (because they have two states at each point - on or off). 16 is a power of 2, so computers can use it as well as they use binary.

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Q: Where do they use hexadecimal system?
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