Add two numbers without using Arithmetic Operators in C++

By Meghana Thatikonda

In this tutorial, we will learn how to add two numbers without using any arithmetic operators along with its implementation in C++.

Add two numbers without using Arithmetic Operators

We wish to add two numbers without using any arithmetic operators like +, -, *, / etc. One way of doing this is by using bitwise operators.

If we have two single-bit binary numbers then we can find their sum by simple half adder logic. That is we get the sum by performing bitwise XOR(exclusive-OR) operation and the carry by performing bitwise AND operation. We can extend this logic to perform the addition of any length binary numbers.

Example:

First binary number     = 1                        First binary number     = 1
Second binary number = 0                        Second binary number = 0
——————————————–                  ——————————————–
Carry (AND)                    = 0                        Sum (XOR)                 = 1
——————————————–                  ——————————————–

Implementation in C++

#include <iostream> 
using namespace std; 

int main() 
{ 
  int num_1, num_2;
  cout << "Enter two numbers ";
  cin >> num_1 >> num_2;
  int carry;
  while (num_2 != 0)
  {
    carry = num_1 & num_2; 
    num_1 = num_1 ^ num_2; 
    num_2 = carry << 1;
  }
  cout << "Sum is " << num_1;  
  return 0; 
}

Consider two numbers 12 and 4 as input and let us see how the code is working.

12 in binary = 1100
4 in binary   = 0100

num_1          = 1100                num_1          = 1100
num_2         = 0100                num_2          = 0100             carry            = 0100
—————————–                 —————————–               ——————————
carry(AND) = 0100                  num_1(XOR) = 1000               num_2(<<1) = 1000
—————————–                —————————–               ——————————

num_1          = 1000                num_1           = 1000
num_2         = 1000                num_2          = 1000             carry            = 01000
—————————–                —————————–               ——————————
carry(AND) = 1000                 num_1(XOR) = 0000             num_2(<<1) = 10000
—————————–                —————————–               ——————————

num_1          = 00000                num_1           = 00000
num_2         = 10000                 num_2          = 10000             carry            = 00000
—————————–                ———————————               ——————————
carry(AND) = 00000                 num_1(XOR) = 10000               num_2(<<1) = 000000
—————————–                ———————————               ——————————

Now, num_2 became zero and we come out of the while loop. And, num_1 = 10000 whose decimal equivalent is 16 i.e., the sum of 12 and 4. In this way, we obtain the sum of two numbers without using any arithmetic operators in C++.

Output:

Enter two numbers 12 4
Sum is 16

Also read, Print prime numbers in C++
Height of a binary tree in C++