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Take each digit in the number, and multiply it by the base in which expressed to the power of the column it's in. Note that the columns, going from right to left, use powers starting at zero and going up by one.

For example, look at any decimal number. Let's try 1976:

1976 = 1000 + 900 + 70 + 6 = 1×103 + 9×102 + 7×101 + 6×100

All bases work the same way, so converting to decimal can be done quite easily. For example, let's take the base 7 number "6143":

6143(7) = 6×73 + 1×72 + 4×71 + 3×70

= 6 × 343 + 1 × 49 + 4 × 7 + 3 × 1

= 2058 + 49 + 28 + 3

= 2138

so "6143" in base 7 is equal to "2138" in decimal.

See the related links for a convenient on-line calculator that will convert them for you.

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15y ago

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