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