Add two integers without using arithmetic operator

Write a function that accepts two unsigned int and return sum of these two integers. The function should not use any arithmetic operator (mayuse bitwise operators only).

Solution:

Using Bitwise operator we can find the Sum-bit of two bits using the XOR operator and Carry-bit using AND operator, as shown below in the truth table

x   y  SUM  CARRY
--  -- ---  -----
0   0   0     0
0   1   1     0
1   0   1     0
1   1   0     1

We can extend this logic (of adding two bits) for large integers. We use the fact that if the two integers have different bits at same positions then XOR (^) will return Sum of these two integers and there will be no carry

a = 5  = 0101
b = 10 = 1010
-------------
XOR    = 1111 = 15 (5+10)

If there are some Common bits, then we can have a combined carry (carry of all the common bits) by taking Bitwise-AND of two numbers. Hence the Algo can be

sum = a;
while(b != 0)
    carry = a AND b
    sum = sum XOR b
    b = carry << 1   // Because Carry of position i' gets added to (i+1)

unsigned int add(unsigned int a, unsigned int b)
{
    while (b != 0)
    {
        int carrb = a & b;
        a = a ^ b;
        b = carrb << 1;
    }
    return a;
}