Check if binary representation of a number is palindrome

Given an integer ‘x’, write a C function that returns true if binary representation of x is palindrome else return false.

For example a numbers with binary representation as 10..01 is palindrome and number with binary representation as 10..00 is not palindrome.

The idea is similar to checking a string is palindrome or not. We start from leftmost and rightmost bits and compare bits one by one. If we find a mismatch, then return false.

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

Algorithm:
isPalindrome(x)
1) Find number of bits in x using sizeof() operator.
2) Initialize left and right positions as 1 and n respectively.
3) Do following while left ‘l’ is smaller than right ‘r’.
..…..a) If bit at position ‘l’ is not same as bit at position ‘r’, then return false.
..…..b) Increment ‘l’ and decrement ‘r’, i.e., do l++ and r–-.
4) If we reach here, it means we didn’t find a mismatching bit.

To find the bit at a given position, we can use the idea similar to this post. The expression “x & (1 << (k-1))” gives us non-zero value if bit at k’th position from right is set and gives a zero value if if k’th bit is not set.

Following is the implementation of the above algorithm.

C/C++

// C++ Program to Check if binary representation 
// of a number is palindrome 
#include<iostream> 
using namespace std; 
  
// This function returns true if k'th bit in x  
// is set (or 1). For example if x (0010) is 2  
// and k is 2, then it returns true 
bool isKthBitSet(unsigned int x, unsigned int k) 
{ 
    return (x & (1 << (k - 1))) ? true : false; 
} 
  
// This function returns true if binary  
// representation of x is palindrome. 
// For example (1000...001) is paldindrome 
bool isPalindrome(unsigned int x) 
{ 
    int l = 1; // Initialize left position 
    int r = sizeof(unsigned int) * 8; // initialize right position 
  
    // One by one compare bits 
    while (l < r) 
    { 
        if (isKthBitSet(x, l) != isKthBitSet(x, r)) 
            return false; 
        l++; r--; 
    } 
    return true; 
} 
  
// Driver Code 
int main() 
{ 
    unsigned int x = 1 << 15 + 1 << 16; 
    cout << isPalindrome(x) << endl; 
    x = 1 << 31 + 1; 
    cout << isPalindrome(x) << endl; 
    return 0; 
} 

Java

// Java Program to Check if binary representation  
// of a number is palindrome  
class GFG  
{ 
  
    // This function returns true if k'th bit in x  
    // is set (or 1). For example if x (0010) is 2  
    // and k is 2, then it returns true  
    static int isKthBitSet(long x, long k)  
    {  
        int rslt = ((x & (1 << (k - 1))) != 0) ? 1 : 0;  
        return rslt; 
    }  
      
    // This function returns true if binary  
    // representation of x is palindrome.  
    // For example (1000...001) is paldindrome  
    static int isPalindrome( long x)  
    {  
        long l = 1; // Initialize left position  
        long r = (Integer.SIZE/8 )* 8; // initialize right position  
      
        // One by one compare bits  
        while (l < r)  
        {  
            if (isKthBitSet(x, l) != isKthBitSet(x, r))  
            { 
                return 0;  
            } 
            l++; r--;  
        }  
        return 1;  
    }  
      
    // Driver Code  
    public static void main (String[] args) 
    {  
        long x = 1 << 15 + 1 << 16 ;  
        System.out.println(isPalindrome(x));  
          
        x = (1 << 31) + 1 ;  
        System.out.println(isPalindrome(x));  
    }  
} 
  
// This code is contributed by AnkitRai01 

Python3

# python 3 Program to Check if binary representation 
# of a number is palindrome 
import sys 
# This function returns true if k'th bit in x  
# is set (or 1). For example if x (0010) is 2  
# and k is 2, then it returns true 
def isKthBitSet(x, k): 
    if ((x & (1 << (k - 1))) !=0): 
        return True
    else: 
        return False
  
# This function returns true if binary  
# representation of x is palindrome. 
# For example (1000...001) is paldindrome 
def isPalindrome(x): 
    l = 1 # Initialize left position 
    r = 2 * 8 # initialize right position 
  
    # One by one compare bits 
    while (l < r): 
        if (isKthBitSet(x, l) != isKthBitSet(x, r)): 
            return False
        l += 1
        r -= 1
      
    return True
  
# Driver Code 
if __name__ =='__main__': 
    x = 1 << 15 + 1 << 16
    print(int(isPalindrome(x))) 
    x = 1 << 31 + 1
    print(int(isPalindrome(x))) 
  
# This code is contributed by 
# Surendra_Gangwar 

C#

// C# Program to Check if binary representation  
// of a number is palindrome  
using System; 
  
class GFG  
{  
  
    // This function returns true if k'th bit in x  
    // is set (or 1). For example if x (0010) is 2  
    // and k is 2, then it returns true  
    static int isKthBitSet(long x, long k)  
    {  
        int rslt = ((x & (1 << (int)(k - 1))) != 0) ? 1 : 0;  
        return rslt;  
    }  
      
    // This function returns true if binary  
    // representation of x is palindrome.  
    // For example (1000...001) is paldindrome  
    static int isPalindrome( long x)  
    {  
        long l = 1; // Initialize left position  
        long r = 4 * 8; // initialize right position  
      
        // One by one compare bits  
        while (l < r)  
        {  
            if (isKthBitSet(x, l) != isKthBitSet(x, r))  
            {  
                return 0;  
            }  
            l++; r--;  
        }  
        return 1;  
    }  
      
    // Driver Code  
    public static void Main ()  
    {  
        long x = 1 << 15 + 1 << 16 ;  
        Console.WriteLine(isPalindrome(x));  
          
        x = (1 << 31) + 1 ;  
        Console.WriteLine(isPalindrome(x));  
    }  
}  
  
// This code is contributed by AnkitRai01  

PHP

<?php 
// PHP Program to Check if binary representation 
// of a number is palindrome 
  
// This function returns true if k'th bit in x  
// is set (or 1). For example if x (0010) is 2  
// and k is 2, then it returns true 
function isKthBitSet($x, $k) 
{ 
    return ($x & (1 << ($k - 1))) ? true : false; 
} 
  
// This function returns true if binary  
// representation of x is palindrome.  
// For example (1000...001) is paldindrome 
function isPalindrome($x) 
{ 
    $l = 1; // Initialize left position 
    $r = sizeof(4) * 8; // initialize right position 
  
    // One by one compare bits 
    while ($l < $r) 
    { 
        if (isKthBitSet($x, $l) != isKthBitSet($x, $r)) 
            return false; 
        $l++;  
        $r--; 
    } 
    return true; 
} 
  
// Driver Code 
$x = 1 << 15 + 1 << 16; 
echo isPalindrome($x), "\n"; 
$x = 1 << 31 + 1; 
echo isPalindrome($x), "\n"; 
  
// This code is contributed by ajit. 
?> 

Output:

1
1

This article is contributed by Saurabh Gupta. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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My Personal Notes

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

C/C++

Java

Python3

C#

PHP

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