How to convert a number from binary ss to quintal ss?

Question

Algorithms

How to convert from 2cc to 5cc.
Namely the number 10101010^2 in ^5
It is important not to use decimal! Thanks

Answer 1

10101010
You need to expand a number with power factors. The exponents, when converted to the fivefold SS, must also be fivefold. Then count the exponents, multiply and add the result. All operations must be done in fivefold SS.
decompose:
1*(2^12)+0*(2^11)+1*(2^10)+0*(2^4)+1*(2^3)+0*(2^2)+ 1*(2^1)+0*(2^0)=
exponentiate:
1*(1003)+0*(224)+1*(112)+0*(31)+1*(13)+ 0*(4)+1*(2)+0*(1)=
multiply:
1003+0+112+0+13+0+2+0=
add:
1140