Problem
1. Draw a TM that takes as input a string of 0's and 1's, interprets it as the binary representation of a nonnegative integer, and leaves as output the unary representation of that integer (i.e., a string of that many 1's).
2. Draw a TM that does the reverse of the previous problem: accepts a string of n 1's as input and leaves as output the binary representation of n.