Sum of Two Integers

Given two integers a and b, return the sum of the two integers without using the operators + and -.

My Solutions:

a ^ b: 代表a和b相加后，应该进位的地方不进位的结果

a	b	a XORb
0	0	0
0	1	1
1	0	1
1	1	0

a & b: 代表a和b都是1的结果; a & b << 1: 代表进位之后的结果

比如a=1(000...001), b=3(000...011)

• a^b=000...010, (a&b)<<1= 000...001<<1 = 000...010 --> a=010, b=010

• a^b=000, (a&b)<<1=010<<1=0100 --> a=000, b=0100

• a^b=0100, (a&b)<<1=0000 --> a=0100, b=0000, stop here

    public int getSum(int a, int b) {
        while (b != 0) {
            int carry = a & b;
            a = a ^ b;
            b = carry << 1;
        }
        return a;
    }