this is right! this is how binary to decimal conversion works. the BNs are the the powers of two: each digit is the previous increased by itself => each digit is the previous multiplied by 2 => nth digit is 2 to the nth power.

positional base for a given B works the same way if you change "add all the powers of two where there is a one" to "add all the powers of K multiplied by the corresponding digit" (these are equivalent if K is 2; multiplying something by 0 is 0)

say you want to get the decimal number of the octal number 5756. let's get the powers that we need:

- 8
^{3}= 512 - 8
^{2}= 64 - 8
^{1}= 8 - 8
^{0}= 1

and 5*512 + 7*64 + 5*8 + 6*1 = 3054. this will work for every octal(/binary) number!