How to add two numbers without using ++ or + or another arithmetic operator

Question

How do I add two numbers without using ++ or + or any other arithmetic operator?

It was a question asked a long time ago in some campus interview. Anyway, today some

Answer 1

Without using any operators adding two integers can be done in different ways as follows:

int sum_of_2 (int a, int b){
   int sum=0, carry=sum;
   sum =a^b;
   carry = (a&b)<<1;
   return (b==0)? a: sum_of_2(sum, carry);
}
// Or you can just do it in one line as follows:
int sum_of_2 (int a, int b){
   return (b==0)? a: sum_of_2(a^b, (a&b)<<1);
}
// OR you can use the while loop instead of recursion function as follows
int sum_of_2 (int a, int b){
    if(b==0){
       return a;
   }
   while(b!=0){
     int sum = a^b;
     int carry = (a&b)<<1;
     a= sum;
     b=carry;
  }
  return a;
}

Answer 2

All arithmetic operations decompose to bitwise operations to be implemented in electronics, using NAND, AND, OR, etc. gates.

Adder composition can be seen here.

Answer 3

Here is a compact C solution. Sometimes recursion is more readable than loops.

int add(int a, int b){
    if (b == 0) return a;
    return add(a ^ b, (a & b) << 1);
}

Answer 4

The following would work.

x - (-y)

Answer 5

int Add(int a, int b)
{
    while (b)
    {
        int carry = a & b;
        a = a ^ b;
        b = carry << 1;
    }
    return a;
}

Answer 6

You could transform an adder circuit into an algorithm. They only do bitwise operations =)