I want to do a division of two binaries and take the rest (mod). But I want to do this using polynomials, let's take the example:
binary dividend: 010001100101000000000000 binary divisor: 100000111
polynomial form dividend: $x^{22}+x^{18}+x^{17}+x^{14}+x^{12}$
polynomial form divisor: $x^8+x^2+x^1+x^0$
after the division: $\frac{x^{22}+x^{18}+x^{17}+x^{14}+x^{12}}{x^8+x^2+x^1+x^1}$
result is: $x^{14}+x^{10}+x^9+x^8+x^7+x^2+x^1$
Remainder is : $x^7+x^4+x^1$
Someone can explain to me, step-by-step, how to do this division? Without convert to binary, needs to be in polynomial form.
Thank you.