Let's say we have an arbitrary number in base $b$, $(x_3x_2x_1x_0)_b$.

We can write the equivalent of this number in base $10$ as follows:

$(x_3x_2x_1x_0)_b = x_3*b^3+x_2*b^2+x_1*b^1+x_0*b^0$

So, let $N = x_3*b^3+x_2*b^2+x_1*b^1+x_0*b^0$

If we want to convert decimal to any other base we just need to remove the

bases $b^3, b^2, b^1, b^0$.

To remove the bases we need to divide by $b$.

$\frac{N}{b} = x_3*b^2+x_2*b^1+x_1*b^0+x_0*b^{-1}$

BUT the result suppose to be:

$\frac{N}{b} = x_3*b^2+x_2*b^1+x_1*b^0+x_0$

and $x_0$ would be the least digit that we are looking for.

I just don't get it!

I've seen it in this video:

https://m.youtube.com/watch?v=QAHyFa3gKKc&t=313s

In the minute 0:28

## Best Answer

You misinterpreted the video.

$\frac{N}{b} = x_3*b^2+x_2*b^1+x_1*b^0$

with a remainder of$x_0.$To take a simpler example, consider dividing $14$ by $3$.

Then $\frac{14}{3} = 4$, with a remainder of $2$.

This implies that $14 = (3 \times 4) + 2.$