Check if all bits of a number are set

Given a number n. The problem is to check whether every bit in the binary representation of the given number is set or not. Here 0 <= n.

Examples :

Input : 7
Output : Yes
(7)₁₀ = (111)₂

Input : 14
Output : No

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

Method 1: If n = 0, then answer is ‘No’. Else perform the two operations until n becomes 0.

While (n > 0)
 If n & 1 == 0, 
     return 'No'
 n >> 1

If loop terminates without returning ‘No’, then all bits are set in the binary representation of n.

C++

// C++ implementation to check whether every 
// digit in the binary representation of the 
// given number is set or not 
#include <bits/stdc++.h> 
using namespace std; 
  
// function to check if all the bits are set 
// or not in the binary representation of 'n' 
string areAllBitsSet(int n) 
{ 
    // all bits are not set 
    if (n == 0) 
        return "No"; 
  
    // loop till n becomes '0' 
    while (n > 0) 
    { 
        // if the last bit is not set 
        if ((n & 1) == 0) 
            return "No"; 
  
        // right shift 'n' by 1 
        n = n >> 1; 
    } 
  
    // all bits are set 
    return "Yes"; 
} 
  
// Driver program to test above 
int main() 
{ 
    int n = 7; 
    cout << areAllBitsSet(n); 
    return 0; 
} 

Java

// java implementation to check  
// whether every digit in the  
// binary representation of the 
// given number is set or not 
import java.io.*; 
  
class GFG { 
      
    // function to check if all the bits 
    // are setthe bits are set or not 
    // in the binary representation of 'n' 
    static String areAllBitsSet(int n) 
    { 
        // all bits are not set 
        if (n == 0) 
            return "No"; 
      
        // loop till n becomes '0' 
        while (n > 0) 
        { 
            // if the last bit is not set 
            if ((n & 1) == 0) 
                return "No"; 
      
            // right shift 'n' by 1 
            n = n >> 1; 
        } 
      
            // all bits are set 
            return "Yes"; 
    } 
      
    // Driver program to test above 
    public static void main (String[] args) { 
    int n = 7; 
      
    System.out.println(areAllBitsSet(n)); 
    } 
} 
  
  
// This code is contributed by vt_m 

Python3

# Python implementation 
# to check whether every 
# digit in the binary 
# representation of the 
# given number is set or not 
  
# function to check if 
# all the bits are set 
# or not in the binary 
# representation of 'n' 
def areAllBitsSet(n): 
  
    # all bits are not set 
    if (n == 0): 
        return "No"
   
    # loop till n becomes '0' 
    while (n > 0): 
      
        # if the last bit is not set 
        if ((n & 1) == 0): 
            return "No"
   
        # right shift 'n' by 1 
        n = n >> 1
      
   
    # all bits are set 
    return "Yes"
  
   
# Driver program to test above 
  
n = 7
print(areAllBitsSet(n)) 
  
# This code is contributed 
# by Anant Agarwal. 

C#

// C# implementation to check  
// whether every digit in the  
// binary representation of the 
// given number is set or not 
using System; 
  
class GFG 
{ 
      
    // function to check if   
    // all the bits are set  
    // or not in the binary 
    // representation of 'n' 
    static String areAllBitsSet(int n) 
    { 
        // all bits are not set 
        if (n == 0) 
            return "No"; 
      
        // loop till n becomes '0' 
        while (n > 0) 
        { 
            // if the last bit 
            // is not set 
            if ((n & 1) == 0) 
                return "No"; 
      
            // right shift 'n' by 1 
            n = n >> 1; 
        } 
      
            // all bits are set 
            return "Yes"; 
    } 
      
    // Driver Code 
    static public void Main () 
    { 
        int n = 7; 
        Console.WriteLine(areAllBitsSet(n)); 
    } 
} 
  
// This code is contributed by ajit 

PHP

<?php 
// PHP implementation to check 
// whether every digit in the  
// binary representation of the 
// given number is set or not 
  
// function to check if all the  
// bits are set or not in the 
// binary representation of 'n' 
function areAllBitsSet($n) 
{ 
    // all bits are not set 
    if ($n == 0) 
        return "No"; 
  
    // loop till n becomes '0' 
    while ($n > 0) 
    { 
        // if the last bit is not set 
        if (($n & 1) == 0) 
            return "No"; 
  
        // right shift 'n' by 1 
        $n = $n >> 1; 
    } 
  
    // all bits are set 
    return "Yes"; 
} 
  
// Driver Code 
$n = 7; 
echo areAllBitsSet($n); 
  
// This code is contributed by aj_36 
?> 

Output :

Yes

Time Complexity : O(d), where ‘d’ is the number of bits in the binary representation of n.

Method 2: If n = 0, then answer is ‘No’. Else add 1 to n. Let it be num = n + 1. If num & (num – 1) == 0, then all bits are set, else all bits are not set.
Explanation: If all bits in the binary representation of n are set, then adding ‘1’ to it will produce a number which will be a perfect power of 2. Now, check whether the new number is a perfect power of 2 or not.

C++

// C++ implementation to check whether every 
// digit in the binary representation of the 
// given number is set or not 
#include <bits/stdc++.h> 
using namespace std; 
  
// function to check if all the bits are set 
// or not in the binary representation of 'n' 
string areAllBitsSet(int n) 
{ 
    // all bits are not set 
    if (n == 0) 
        return "No"; 
  
    // if true, then all bits are set 
    if (((n + 1) & n) == 0) 
        return "Yes"; 
  
    // else all bits are not set 
    return "No"; 
} 
  
// Driver program to test above 
int main() 
{ 
    int n = 7; 
    cout << areAllBitsSet(n); 
    return 0; 
} 

Java

// JAVA implementation to check whether  
// every digit in the binary representation  
// of the given number is set or not 
import java.io.*; 
  
class GFG { 
      
    // function to check if all the  
    // bits are set or not in the  
    // binary representation of 'n' 
    static String areAllBitsSet(int n) 
    { 
        // all bits are not set 
        if (n == 0) 
            return "No"; 
      
        // if true, then all bits are set 
        if (((n + 1) & n) == 0) 
            return "Yes"; 
      
        // else all bits are not set 
        return "No"; 
    } 
      
    // Driver program to test above 
    public static void main (String[] args) { 
    int n = 7; 
    System.out.println(areAllBitsSet(n)); 
    } 
} 
  
// This code is contributed by vt_m 

Python3

# Python implementation to 
# check whether every 
# digit in the binary 
# representation of the 
# given number is set or not 
  
# function to check if 
# all the bits are set 
# or not in the binary 
# representation of 'n' 
def areAllBitsSet(n): 
  
    # all bits are not set 
    if (n == 0): 
        return "No"
   
    # if true, then all bits are set 
    if (((n + 1) & n) == 0): 
        return "Yes"
   
    # else all bits are not set 
    return "No"
  
   
# Driver program to test above 
  
n = 7
print(areAllBitsSet(n)) 
  
# This code is contributed 
# by Anant Agarwal. 

C#

// C# implementation to check  
// whether every digit in the  
// binary representation of  
// the given number is set or not 
using System; 
  
class GFG 
{ 
      
    // function to check if all the  
    // bits are set or not in the  
    // binary representation of 'n' 
    static String areAllBitsSet(int n) 
    { 
        // all bits are not set 
        if (n == 0) 
            return "No"; 
      
        // if true, then all 
        // bits are set 
        if (((n + 1) & n) == 0) 
            return "Yes"; 
      
        // else all bits are not set 
        return "No"; 
    } 
      
    // Driver Code 
    static public void Main () 
    { 
        int n = 7; 
        Console.WriteLine(areAllBitsSet(n)); 
    } 
} 
  
// This code is contributed by m_kit 

PHP

<?php 
// PHP implementation to check  
// whether every digit in the  
// binary representation of the 
// given number is set or not 
  
// function to check if all  
// the bits are set or not in  
// the binary representation of 'n' 
function areAllBitsSet($n) 
{ 
    // all bits are not set 
    if ($n == 0) 
        return "No"; 
  
    // if true, then all 
    // bits are set 
    if ((($n + 1) & $n) == 0) 
        return "Yes"; 
  
    // else all bits  
    // are not set 
    return "No"; 
} 
  
// Driver Code 
$n = 7; 
echo areAllBitsSet($n); 
  
// This code is contributed by ajit 
?> 

Output :

Yes

References:
https://www.careercup.com/question?id=9503107

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