Converting from Base-2 numbers to any base Is there any general method to convert from base-2 to any base.
When we convert from base-2 to base-10, we do the sum of weights corresponding to position with 1.
For Example, $(1101)_2 $, the decimal representation will be $ 1*(2^3)_{10} + 1*(2^2)_{10} 
+ 0*(2^1)_{10} + 1*(2^0)_{10} = (13)_{10} $ and this summation is calculated in base-10.
So for base-2 to any base-n conversion, can i write $ 1*(2^3)_{n} + 1*(2^2)_{n} 
+ 0*(2^1)_{n} + 1*(2^0)_{n} $. where $ 2^i $ and the summation will be calculated in base-n.
Example: Converting $(1101)_2$ to base-6.
$ =  1*(2^3)_{6} + 1*(2^2)_{6} + 0*(2^1)_{6} + 1*(2^0)_{6} $
$ = (21)_6 $
Is this true for any n > 2 ?
 A: Yes, it is true that
$$(1101)_2 =  1\times(2^3)_n + 1\times(2^2)_n + 0\times(2^1)_n + 1\times(2^0)_n $$
for any integer base $n > 1.$
And it is true that (provided that you consistently use base-$n$ representations of all intermediate results and correctly do base-$n$ arithmetic on their digits)
you will get the correct base-$n$ representation of $(1101)_2$ in the end.
For example,
$$(1101)_2 = 1\times(2^3)_6 + 1\times(2^2)_6 + 0\times(2^1)_6 + 1\times(2^0)_6 
 = (21)_6 $$
exactly as you thought.
The reason for this is that the meaning of the notation
$(1101)_2$ is the sum of one times the third power of two,
one times the second power of two, zero times the first power of two,
and one times the zeroth power of two.
It is defined that way in terms of the numbers we call zero, one, two, three, and so forth, and this definition is completely independent of the way the numbers are written.
So as long as you are always using the correct numbers in your calculations,
it doesn't matter that you decided to write them in base six instead of base ten.
The question Converting from base $x$ to base $y$ came close to demonstrating this principle for the conversion of
$(2132)^4$ to base six, but neglected the fact that you have to do the calculations on the right side in base six (not all in base ten) in order for this to work.
This error was pointed out in the comments.

In the related questions, other answers to how to do the conversion come up with algorithms that appear slightly different because they use the definition in a different way.
For example, one popular method for base conversion is to write the number this way:
$$(1101)_2 = ((1\times2 + 1)\times2 + 0)\times2 + 1. $$
This is just a different way of computing the exponents:
$$((1\times2 + 1)\times2 + 0)\times2 + 1 = 1\times2^3 + 1\times2^2 + 0\times2 + 1.$$
Another popular method for converting a base is to divide the input number by the target base with remainder, repeatedly.
The sequence of remainders gives you the digits of the output representation from right to left.
These other algorithms likewise can be used for direct conversion between any two bases as long as you work the arithmetic in the desired target base instead of base ten.
That fact is explained in the answers to the related questions, in particular
Question on type conversion in number system and
Converting between number systems without using mid-conversion.
