Question

I am trying to recursively convert int to binary string but I don’t really understand how the whole positive int to binary string conversion works.

Also found out that apparently each position is like a representation of the power of 2.

Any explanation as to how to convert a positive int to a string representation as shown in the Googled example above is extremely helpful.

Answer 1

Here is a recursive implementation for converting an int to a binary string, which is what I think this question is asking for:

def recursive_bin(i):
    if i == 0:
        return ''
    elif i < 0:
        return '-' + recursive_bin(-i)
    else:
        return recursive_bin(i>>1) + str(i&1)

Note that this is only useful as an exercise in recursion, if you are just trying to get at the binary string use the built-in bin() function.

This works because i&1 will give you the last bit in i (either 0 or 1), and i>>1 will shift all bits in i to the right by one bit (equivalent to division by 2). Here is an explanation of how this would work for 6 (110₂):

# 6 is 110 in binary
recursive_bin(6)
recursive_bin(6>>1) + str(6 & 1)        -> recursive_bin(3) + '0'
recursive_bin(3>>1) + str(3 & 1) + '0'  -> recursive_bin(1) + '1' + '0'
recursive_bin(1>>1) + str(1 & 1) + '10' -> recursive_bin(0) + '1' + '10'
recursive_bin(0) + '110'                -> '' + '110'
# Final result is '110', since the base case of 0 returns an empty string