Using Python

In the decimal system (base 10), a natural number is represented as a sequence dndn?1 . . . d0 of (decimal) digits, each of which is in the range 0..9. The value of the number is d0 100 +d1 101 ++ dn 10n. Similarly, in the binary system (base 2), a natural number is represented as a sequence bnbn?1 b0 of (binary) digits, each of which is 0 or 1. The value of the number is b0 20 +b1 21 ++bn 2n. For example, the value of the number whose binary representation is 101 is: 120+021+122 =1+0+4=5.

(i) Without using any built-in functions for converting numbers, write a function that takes as input the binary representation of a positive integer n and returns its decimal representation.