Add two numbers without using arithmetic operators (original) (raw)

Last Updated : 11 Sep, 2024

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Given two integers **a and **b, the task is to find the sum of a and b without using + or – operators.

**Examples:

**Input: a = 10, b = 30
**Output: 40

**Input: a = -1, b = 2
**Output: 1

**Approach:

The approach is to add two numbers using bitwise operations. Let’s first go through some observations:

• **a & b will have only those bits set which are set in both **a and **b.
• **a ^ b will have only those bits set which are set in either **a or **b but not in both.

If we want to calculate the sum of a and b such that a and b has **no common set bit, then **a ^ b is same as **a + b. So, we can say that **a + b without carry = a ^ b.

**How to handle the case when we have carry, that is a and b has common set bits?

To calculate the carry, we know that carry will only have the **common set bits of a and b, **shifted 1 place to the left. So, we can say that **carry = (a & b) << 1.

Now, the problem is reduced to calculating the sum of ****(a + b without carry)** and **carry. This is again the same problem: sum of two numbers where the **first **number = ****(a + b without carry)** and **second number = **carry. So, we can repeatedly calculate **carry and **sum without carry, till carry is not reduced to 0.

**Working:

**Note: The above approach will work perfectly for languages like C++, Java, C# and JavaScript in which an integer has a size of 32 bits but in Python, we need to handle the overflow separately by creating a 32-bit mask of 1’s.

Below is the implementation of the above algorithm:

C++ `

// C++ Program to add two numbers without using arithmetic operators

#include <bits/stdc++.h> using namespace std;

// function to add two numbers without using arithmetic operators int sum(int a, int b) {

// Iterate till there is no carry 
while (b != 0) { 
    
    // carry contains common set bits of a and b, left shifted by 1
    int carry = (a & b) << 1;

    // Update a with (a + b without carry)
    a = a ^ b;
  
    // Update b with carry
    b = carry; 
} 
return a;

}

int main() { int a = -1, b = 2;

cout << sum(a, b);
return 0; 

}

C

// C Program to add two numbers without using arithmetic operators

#include <stdio.h>

// function to add two numbers without using arithmetic operators int sum(int a, int b) {

// 32 bit mask in hexadecimal
long mask = 0xffffffff;

// Iterate till there is no carry 
while ((b & mask) != 0) { 
    
    // carry contains common set bits of a and b, left shifted by 1
    int carry = ((a & b) & mask) << 1;

    // Update a with (a + b without carry)
    a = a ^ b;
  
    // Update b with carry
    b = carry; 
} 
return a & mask;

}

int main() { int a = -1, b = 2;

printf("%d\n", sum(a, b));
return 0; 

}

Java

// Java Program to add two numbers without using arithmetic operators

class GfG {

// function to add two numbers without using arithmetic operators
static int sum(int a, int b) {
    
    // Iterate till there is no carry 
    while (b != 0) { 
        
        // carry contains common set bits of a and b, left shifted by 1
        int carry = (a & b) << 1;

        // Update a with (a + b without carry)
        a = a ^ b;
      
        // Update b with carry
        b = carry; 
    } 
    return a;
} 

public static void main(String[] args) {
    int a = -1, b = 2;
  
    System.out.println(sum(a, b));
} 

}

Python

Python Program to add two numbers without using arithmetic operators

function to add two numbers without using arithmetic operators

def sum(a, b):

# 32 bit mask in hexadecimal
mask = 0xffffffff

# Iterate till there is no carry 
while (b & mask) != 0:
    
    # carry contains common set bits of a and b, left shifted by 1
    carry = (a & b) << 1

    # Update a with (a + b without carry)
    a = a ^ b
  
    # Update b with carry
    b = carry 

return a & mask if b > 0 else a

a = -1 b = 2

print(sum(a, b))

C#

// C# Program to add two numbers without using arithmetic operators

using System;

class GfG {

// function to add two numbers without using arithmetic operators
static int Sum(int a, int b) {
    
    // Iterate till there is no carry 
    while (b != 0) {
        
        // carry contains common set bits of a and b, left shifted by 1
        int carry = (a & b) << 1;

        // Update a with (a + b without carry)
        a = a ^ b;

        // Update b with carry
        b = carry;
    }
    return a;
}

static void Main() {
    int a = -1, b = 2;

    Console.WriteLine(Sum(a, b));
}

}

JavaScript

// JavaScript Program to add two numbers without using arithmetic operators

// function to add two numbers without using arithmetic operators function sum(a, b) {

// Iterate till there is no carry 
while (b !== 0) {
    
    // carry contains common set bits of a and b, left shifted by 1
    let carry = (a & b) << 1;

    // Update a with (a + b without carry)
    a = a ^ b;
  
    // Update b with carry
    b = carry; 
} 
return a;

}

const a = -1, b = 2;

console.log(sum(a, b));

`

**Time Complexity: O(max(number of bits in a, number of bits in b))
**Auxiliary Space: O(1)