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## Math

Last Updated: Nov 17, 2023
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# Base conversions for base N

A base N number system has N digits. The process of conversion of N based number to decimal and vice versa is very similar to the binary number system process we just saw.
The only thing that changes is that 2 is replaced by N.
So, if the N based number system representation is `An An-1 ... A2 A1 A0`, then the corresponding decimal value is

``````    A0 * N^0 + A1 * N^1 + A2 * N^2 + ...
``````

The reverse process is also exactly similar. We keep dividing by N, keeping track of the remainders as we go.

Let us say our number is `357`, and `N = 7`.

``````                1       R0
---------
7 |  7       R2
---------
7 |  51      R0
---------
7 |  357
``````

Thus the number converts to `1020` in base 7.

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