Program to invert bits of a number Efficiently

Difficulty Level : Medium
Last Updated : 28 Apr, 2021

Given a non-negative integer N. The task is to invert the bits of the number N and print the decimal equivalent of the number obtained after inverting the bits.
Note: Leading 0’s are not being considered.
Examples:

Input : 11
Output : 4
(11)₁₀ = (1011)₂
After inverting the bits, we get:
(0100)₂ = (4)₁₀.

Input : 20
Output : 11
(20)₁₀ = (10100)₂.
After inverting the bits, we get:
(01011)₂ = (11)₁₀.

A similar problem is already discussed in Invert actual bits of a number.
In this article, an efficient approach using bitwise operators is discussed. Below is the step by step algorithm to solve the problem:

Calculate the total number of bits in the given number. This can be done by calculating:
```
X = log₂N
```
Where N is the given number and X is the total number of bits of N.
The next step is to generate a number with X bits and all bits set. That is, 11111….X-times. This can be done by calculating:
```
Step-1: M = 1 << X
Step-2: M = M | (M-1)
```
Where M is the required X-bit number with all bits set.
The final step is to calculate the bit-wise XOR of M with N, which will be our answer.

Below is the implementation of the above approach:

C++

// C++ program to invert actual bits 
// of a number. 
#include <bits/stdc++.h> 
  
using namespace std; 
  
// Function to invert bits of a number 
int invertBits(int n) 
{ 
    // Calculate number of bits of N-1; 
    int x = log2(n) ; 
  
    int m = 1 << x; 
  
    m = m | m - 1; 
  
    n = n ^ m; 
  
    return n; 
} 
  
// Driver code 
int main() 
{ 
    int n = 20; 
  
    cout << invertBits(n); 
  
    return 0; 
} 

Java

// Java program to invert  
// actual bits of a number.  
import java.util.*; 
  
class GFG 
{ 
// Function to invert  
// bits of a number  
static int invertBits(int n)  
{  
    // Calculate number of bits of N-1;  
    int x = (int)(Math.log(n) /  
                  Math.log(2)) ;  
  
    int m = 1 << x;  
  
    m = m | m - 1;  
  
    n = n ^ m;  
  
    return n;  
}  
  
// Driver code  
public static void main(String[] args)  
{  
    int n = 20;  
  
    System.out.print(invertBits(n));  
} 
}  
  
// This code is contributed by Smitha 

Python3

# Python3 program to invert actual 
# bits of a number. 
import math 
  
# Function to invert bits of a number 
def invertBits(n): 
      
    # Calculate number of bits of N-1 
    x = int(math.log(n, 2)) 
  
    m = 1 << x 
  
    m = m | m - 1
  
    n = n ^ m 
  
    return n 
  
# Driver code 
n = 20
  
print(invertBits(n)) 
  
# This code is contributed 29AjayKumar 

C#

// C# program to invert  
// actual bits of a number.  
using System; 
  
  
   
public class GFG 
{ 
// Function to invert  
// bits of a number  
static int invertBits(int n)  
{  
    // Calculate number of bits of N-1;  
    int x = (int)(Math.Log(n) /  
                  Math.Log(2)) ;  
   
    int m = 1 << x;  
   
    m = m | m - 1;  
   
    n = n ^ m;  
   
    return n;  
}  
   
// Driver code  
public static void Main()  
{  
    int n = 20;  
   
    Console.Write(invertBits(n));  
} 
}  
   
// This code is contributed by Subhadeep 

PHP

<?php 
// PHP program to invert actual  
// bits of a number. 
  
// Function to invert bits  
// of a number 
function invertBits($n) 
{ 
    // Calculate number of 
    // bits of N-1; 
    $x = log($n, 2); 
  
    $m = 1 << $x; 
  
    $m = $m | $m - 1; 
  
    $n = $n ^ $m; 
  
    return $n; 
} 
  
// Driver code 
$n = 20; 
  
echo(invertBits($n)); 
  
// This code is contributed  
// by mits 
?> 

Javascript

<script> 
  
// Javascript program to invert actual bits 
// of a number. 
  
// Function to invert bits of a number 
function invertBits(n) 
{ 
    // Calculate number of bits of N-1; 
    let x = parseInt(Math.log(n) / Math.log(2)) ; 
  
    let m = 1 << x; 
  
    m = m | m - 1; 
  
    n = n ^ m; 
  
    return n; 
} 
  
// Driver code 
    let n = 20; 
  
    document.write(invertBits(n)); 
  
</script>

Output:

Time Complexity: O(log₂n)
Auxiliary Space: O(1)

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Table of Contents

Program to invert bits of a number Efficiently

C++

Java

Python3

C#

PHP

Javascript

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