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I understand the basic but what I dont understand is this:

so base 16 to base 10

357/16 = 22.3125 but on this example im looking at says remainder 5?

Ceri Westcott
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    The quotient from dividing 357 by 16 is 22. The remainder is five. This means that 357 = 22 x 16 + 5. The real-valued expression 357/16 is equal to 22.3125, but that's something different. When changing bases, the (integer) quotient and remainder are more useful than the real-valued result of dividing the real numbers. – Patrick87 Oct 13 '14 at 20:28
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    @Ceri Your title mentions base 8, while the body mentions base 10. Which did you mean? – Yuval Filmus Oct 13 '14 at 21:21

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The trick in converting from hexadecimal (base 16) to octal (base 8) is using a (perhaps imaginary) binary (base 2) intermediate. To demonstrate this, let's convert from base 10000 to base 1000, where the intermediate would be decimal (base 10). Consider this number, whose digits are separated by a space:

3 1415 9265 3589 7932 3846

The corresponding number in base 1000 is

314 159 265 358 979 323 846

This example is not completely academic. In some situations one converts between base 1000, used in many European languages, and base 10000, used in Chinese.

Yuval Filmus
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