Add Binary

'''
Full Adder Logic:
S = Cin ^ X ^ Y
Cout = Cin&X + X&Y + Y&Cin
Final Result = Cout.S(final)
Initial c = 0, s = 0
'''
class Solution:
    def addBinary(self, a: str, b: str) -> str:
        cin = 0
        res = []
        m, n = len(a), len(b)
        for i in range(max(m, n)):
            s = cin
            cout = 0
            if i < m:
                x = int(a[-i-1])
                s ^= x
                cout |= cin & x
            if i < n:
                y = int(b[-i-1])
                s ^= y
                cout |= cin & y
            if i < m and i < n:
                cout |= x & y
            res.append(str(s))
            cin = cout
        if cin:
            res.append(str(cin))
        return ''.join(res[::-1])