Sum of Two Integers

'''
Logic:
sum of 010 and 101 is 111 and xor of 010 and 101 is also same.
but sum and xor of 001 and 001 is not same because lsb bits sum ie. 1+1 =0 and 1 carry.
so we will do xor of a and b in a so a will be having the sum of those bits where there
is no carry.we can find the carry bits using & opearator.ofcourse we shift carry while
sum 1 bit so do the same and add carry again.

Here we are using unsigned for keeping that is must otherwise shifting will go overflow.

mask is used here because negative numbers can go more than 32 bits
'''

class Solution:
    def getSum(self, a: int, b: int) -> int:
        MASK = 0xFFFFFFFF
        MAX_INT = 0x7FFFFFFF #maximum possible number in 32 bit ie. 2^32-1 or 01111111 11111111 11111111 11111111

        while b != 0: #addition happens normally,sum the bits and add carry in one left like we do normally
            carry = (a & b) & MASK
            a = (a ^ b) & MASK
            b = (carry << 1) & MASK

        # convert back to signed integer
        return a if a <= MAX_INT else ~(a ^ MASK) #when a=negative number then it will be larger than 32 bit but python thinks it is a positive number,so masking ro bringing to the 32 bit and then fliping to make it negative number