Check if binary representation of a number is palindrome
Last Updated :
23 Feb, 2025
Given an integer x, determine whether its binary representation is a palindrome. Return true if it is a palindrome; otherwise, return false.
Input: x = 9
Output: true
Explanation: The binary representation of 9
is 1001
, which is a palindrome.
Input: x = 10
Output: false
Explanation: The binary representation of 10
is 1010
, which is not a palindrome.
Compare Bits from Both Ends - O(n) Time and O(1) Space
The idea is to compare the bits of x symmetrically from both ends, just like checking if a string is a palindrome. If all corresponding bits match, the binary representation is a palindrome.
Steps to implement the above idea:
- Find the number of bits in x.
- Set l = 1 (leftmost bit) and r = n (rightmost bit).
- While l < r, compare bits at positions l and r.
- If they are different, return false; otherwise, continue.
- If the loop completes without mismatches, return true.
Below is the implementation of the above approach:
C++
// C++ Program to Check if binary representation
// of a number is palindrome
#include <bits/stdc++.h>
using namespace std;
// Function to check if binary representation is a palindrome
bool isBinaryPalindrome(int x) {
int n = log2(x) + 1; // Find number of bits
int l = 0, r = n - 1;
while (l < r) {
// Compare bits at positions l and r
if (((x >> l) & 1) != ((x >> r) & 1)) {
return false;
}
l++;
r--;
}
return true;
}
int main() {
cout << (isBinaryPalindrome(9) ? "true" : "false") << endl;
cout << (isBinaryPalindrome(10) ? "true" : "false") << endl;
return 0;
}
Java
// Java Program to Check if binary representation
// of a number is palindrome
class GfG {
// Function to check if binary representation is a palindrome
static boolean isBinaryPalindrome(int x) {
int n = (int)(Math.log(x) / Math.log(2)) + 1; // Find number of bits
int l = 0, r = n - 1;
while (l < r) {
// Compare bits at positions l and r
if (((x >> l) & 1) != ((x >> r) & 1)) {
return false;
}
l++;
r--;
}
return true;
}
public static void main(String[] args) {
System.out.println(isBinaryPalindrome(9) ? "true" : "false");
System.out.println(isBinaryPalindrome(10) ? "true" : "false");
}
}
Python
import math
# Function to check if binary representation is a palindrome
def is_binary_palindrome(x):
n = int(math.log2(x)) + 1 # Find number of bits
l, r = 0, n - 1
while l < r:
# Compare bits at positions l and r
if ((x >> l) & 1) != ((x >> r) & 1):
return False
l += 1
r -= 1
return True
if __name__ == "__main__":
print("true" if is_binary_palindrome(9) else "false")
print("true" if is_binary_palindrome(10) else "false")
C#
// C# Program to Check if binary representation
// of a number is palindrome
using System;
class GfG {
// Function to check if binary representation is a palindrome
public static bool IsBinaryPalindrome(int x) {
int n = (int)(Math.Log(x) / Math.Log(2)) + 1; // Find number of bits
int l = 0, r = n - 1;
while (l < r) {
// Compare bits at positions l and r
if (((x >> l) & 1) != ((x >> r) & 1)) {
return false;
}
l++;
r--;
}
return true;
}
public static void Main() {
Console.WriteLine(IsBinaryPalindrome(9) ? "true" : "false");
Console.WriteLine(IsBinaryPalindrome(10) ? "true" : "false");
}
}
JavaScript
// Function to check if binary representation is a palindrome
function isBinaryPalindrome(x) {
let n = Math.floor(Math.log2(x)) + 1; // Find number of bits
let l = 0, r = n - 1;
while (l < r) {
// Compare bits at positions l and r
if (((x >> l) & 1) !== ((x >> r) & 1)) {
return false;
}
l++;
r--;
}
return true;
}
console.log(isBinaryPalindrome(9) ? "true" : "false");
console.log(isBinaryPalindrome(10) ? "true" : "false");
Time Complexity: O(n), where n is the number of bits in the binary representation.
Space Complexity: O(1) as only a few integer variables are used.
Using reverse() Function - O(n) Time and O(n) Space
The idea is to convert the integer into its binary representation as a string and then check if the string is a palindrome using the reverse() function.
Steps to implement the above idea:
- Convert the given integer x into its binary representation (without the 0b prefix).
- Store the binary string in a variable.
- Reverse the binary string using the reverse() function or equivalent.
- Compare the original binary string with its reversed version.
- If both strings are equal, return true; otherwise, return false.
Below is the implementation of the above approach:
C++
// C++ program to check if binary representation
// of a number is palindrome
#include <bits/stdc++.h>
using namespace std;
// Function to check if binary representation is a palindrome
bool isBinaryPalindrome(int x) {
string binary = bitset<32>(x).to_string(); // Convert to binary
binary = binary.substr(binary.find('1')); // Remove leading zeros
string revBinary = binary;
reverse(revBinary.begin(), revBinary.end()); // Reverse the string
return binary == revBinary; // Check if palindrome
}
int main() {
cout << (isBinaryPalindrome(9) ? "true" : "false") << endl;
cout << (isBinaryPalindrome(10) ? "true" : "false") << endl;
return 0;
}
Java
// Java program to check if binary representation
// of a number is palindrome
import java.util.*;
class GfG {
// Function to check if binary representation is a palindrome
static boolean isBinaryPalindrome(int x) {
String binary = Integer.toBinaryString(x); // Convert to binary
String revBinary = new StringBuilder(binary).reverse().toString(); // Reverse the string
return binary.equals(revBinary); // Check if palindrome
}
public static void main(String[] args) {
System.out.println(isBinaryPalindrome(9) ? "true" : "false");
System.out.println(isBinaryPalindrome(10) ? "true" : "false");
}
}
Python
# Python program to check if binary representation
# of a number is palindrome
# Function to check if binary representation is a palindrome
def is_binary_palindrome(x):
# Convert to binary and remove '0b'
binary = bin(x)[2:]
# Reverse and compare
return binary == binary[::-1]
if __name__ == "__main__":
print("true" if is_binary_palindrome(9) else "false")
print("true" if is_binary_palindrome(10) else "false")
C#
// C# program to check if binary representation
// of a number is palindrome
using System;
class GfG {
// Function to check if binary representation is a palindrome
public static bool IsBinaryPalindrome(int x) {
string binary = Convert.ToString(x, 2); // Convert to binary
char[] revBinary = binary.ToCharArray();
Array.Reverse(revBinary); // Reverse the string
return binary == new string(revBinary); // Check if palindrome
}
public static void Main() {
Console.WriteLine(IsBinaryPalindrome(9) ? "true" : "false");
Console.WriteLine(IsBinaryPalindrome(10) ? "true" : "false");
}
}
JavaScript
// JavaScript program to check if binary representation
// of a number is palindrome
// Function to check if binary representation is a palindrome
function isBinaryPalindrome(x) {
let binary = x.toString(2); // Convert to binary
let revBinary = binary.split("").reverse().join(""); // Reverse the string
return binary === revBinary; // Check if palindrome
}
console.log(isBinaryPalindrome(9) ? "true" : "false");
console.log(isBinaryPalindrome(10) ? "true" : "false");
Time Complexity: O(n), where n is the number of bits in the binary representation (at most 32).
Space Complexity: O(n) due to storing the binary string and its reverse.
Using OR to find Reverse - O(logn) Time and O(1) Space
This approach uses bitwise operations to reverse the binary representation of a number and then checks if it is equal to the original binary representation, indicating whether or not it is a palindrome.
Steps to implement the above idea:
- Create a copy of the input number and initialize a variable to hold the reversed binary representation.
- Loop through the bits of the input number and append each bit to the reversed binary representation.
- Convert the reversed binary representation to an integer and compare it with the original number.
- If the two numbers are equal, return true, else return false.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
// Function to check if binary representation is a palindrome
bool isBinaryPalindrome(int x) {
int rev = 0, temp = x;
while (temp > 0) {
rev = (rev << 1) | (temp & 1); // Append LSB to rev
temp >>= 1; // Shift temp right
}
return x == rev; // Compare reversed with original
}
int main() {
cout << (isBinaryPalindrome(9) ? "true" : "false") << endl;
cout << (isBinaryPalindrome(10) ? "true" : "false") << endl;
return 0;
}
Java
class GfG {
// Function to check if binary representation is a palindrome
static boolean isBinaryPalindrome(int x) {
int rev = 0, temp = x;
while (temp > 0) {
rev = (rev << 1) | (temp & 1); // Append LSB to rev
temp >>= 1; // Shift temp right
}
return x == rev; // Compare reversed with original
}
public static void main(String[] args) {
System.out.println(isBinaryPalindrome(9) ? "true" : "false");
System.out.println(isBinaryPalindrome(10) ? "true" : "false");
}
}
Python
# Function to check if binary representation is a palindrome
def is_binary_palindrome(x):
rev, temp = 0, x
while temp > 0:
rev = (rev << 1) | (temp & 1) # Append LSB to rev
temp >>= 1 # Shift temp right
return x == rev # Compare reversed with original
if __name__ == "__main__":
print("true" if is_binary_palindrome(9) else "false")
print("true" if is_binary_palindrome(10) else "false")
C#
using System;
class GfG {
// Function to check if binary representation is a palindrome
public static bool IsBinaryPalindrome(int x) {
int rev = 0, temp = x;
while (temp > 0) {
rev = (rev << 1) | (temp & 1); // Append LSB to rev
temp >>= 1; // Shift temp right
}
return x == rev; // Compare reversed with original
}
public static void Main() {
Console.WriteLine(IsBinaryPalindrome(9) ? "true" : "false");
Console.WriteLine(IsBinaryPalindrome(10) ? "true" : "false");
}
}
JavaScript
// Function to check if binary representation is a palindrome
function isBinaryPalindrome(x) {
let rev = 0, temp = x;
while (temp > 0) {
rev = (rev << 1) | (temp & 1); // Append LSB to rev
temp >>= 1; // Shift temp right
}
return x === rev; // Compare reversed with original
}
console.log(isBinaryPalindrome(9) ? "true" : "false");
console.log(isBinaryPalindrome(10) ? "true" : "false");
Time Complexity: O(log n), where n is the value of the input number.
Auxiliary Space: O(1), for storing the loop variable and reversed binary representation.
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