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# 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)

**Code:**

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

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