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Find average of two numbers using bit operation

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  • Last Updated : 30 May, 2022
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Given two integers x and y, the task is to find the average of these numbers i.e. (x + y) / 2 using bit operations. Note that this method will give result as floor value of the calculated average.
Examples: 
 

Input: x = 2, y = 4 
Output:
(2 + 4) / 2 = 3
Input: x = 10, y = 9 
Output:
 

 

Approach: Average of two numbers x and y can be calculated using bit operations as: 
 

(x & y) + ((x ^ y) >> 1) 
 

where & is bitwise AND, ^ is bitwise XOR and >> 1 is right shift by 1 bit.
Below is the implementation of the above approach:
 

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the average
// of x and y using bit operations
int getAverage(int x, int y)
{
    // Calculate the average
    // Floor value of (x + y) / 2
    int avg = (x & y) + ((x ^ y) >> 1);
 
    return avg;
}
 
// Driver code
int main()
{
    int x = 10, y = 9;
 
    cout << getAverage(x, y);
 
    return 0;
}

Java




// Java implementation of the approach
class GFG {
 
    // Function to return the average
    // of x and y using bit operations
    static int getAverage(int x, int y)
    {
 
        // Calculate the average
        // Floor value of (x + y) / 2
        int avg = (x & y) + ((x ^ y) >> 1);
 
        return avg;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int x = 10, y = 9;
 
        System.out.print(getAverage(x, y));
    }
}

Python




# Python 3 implementation of the approach
 
# Function to return the average
# of x and y using bit operations
def getAverage(x, y):
 
    # Calculate the average
    # Floor value of (x + y) / 2
    avg = (x & y) + ((x ^ y) >> 1);
     
    return avg
 
# Driver code
x = 10
y = 9
print(getAverage(x, y))

C#




// C# implementation of the approach
using System;
 
class GFG
{
 
    // Function to return the average
    // of x and y using bit operations
    static int getAverage(int x, int y)
    {
 
        // Calculate the average
        // Floor value of (x + y) / 2
        int avg = (x & y) + ((x ^ y) >> 1);
 
        return avg;
    }
 
    // Driver code
    public static void Main()
    {
        int x = 10, y = 9;
 
        Console.WriteLine(getAverage(x, y));
    }
}
 
// This code is contributed by AnkitRai01

PHP




<?php
// PHP implementation of the approach
 
// Function to return the average
// of x and y using bit operations
function getAverage($x, $y)
{
    // Calculate the average
    // Floor value of (x + y) / 2
    $avg = ($x & $y) + (($x ^ $y) >> 1);
 
    return $avg;
}
 
// Driver code
    $x = 10;
    $y = 9;
 
    echo getAverage($x, $y);
 
// This code is contributed by ajit.
?>

Javascript




<script>
// javascript implementation of the approach   
 
    // Function to return the average
    // of x and y using bit operations
    function getAverage(x , y)
    {
 
        // Calculate the average
        // Floor value of (x + y) / 2
        var avg = (x & y) + ((x ^ y) >> 1);
 
        return avg;
    }
 
    // Driver code
    var x = 10, y = 9;
    document.write(getAverage(x, y));
 
// This code is contributed by Rajput-Ji
</script>

Output: 

9

 

Time Complexity: O(1)

Auxiliary Space: O(1)


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