Python: add binary numbers represented in a string recursively

addbinary.py

def add_binary(n, m, c=False):
    nb = n[-1] == "1" if n else False
    mb = m[-1] == "1" if m else False
    r = nb ^ mb ^ c
    c = not nb and mb and c or nb and (mb or c)
    n2 = n[:-1] if n else n
    m2 = m[:-1] if m else m
    if not n and not m:
        return ""
    return add_binary(n2, m2, c) + ("1" if r else "0")