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# 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.

#### Method#1:  We follow the following logic to check binary of number is Palindrome or not:

• Find number of bits in x using sizeof() operator.
• Initialize left and right positions as 1 and n respectively.
• Do following while left ‘l’ is smaller than right ‘r’.
• If bit at position ‘l’ is not same as bit at position ‘r’, then return false.
• Increment ‘l’ and decrement ‘r’, i.e., do l++ and r–-.
•  If we reach here, it means we didn’t find a mismatching bit.
• To find the bit at a given position, we can use an 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++ Program to Check if binary representation``// of a number is palindrome``#include``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 palindrome``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 palindrome``    ``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 palindrome``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 palindrome``    ``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

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## Javascript

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Output

```1
1```

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

Method#2: Using reverse() function:

• When user inputs an integer, it is passed to method which will evaluate the result.
• Actual logic inside the method focuses on following:
• It first convert the integer to binary form of integer in string format.
• It reverse the string using reverse method.
• It is palindrome if both the string is equal else not.

Below is the implementation of the above approach:

## C++

 `// C++ program to check if binary representation``// of a number is palindrome``#include ``using` `namespace` `std;` `// This function return the binary form of integer in string format``string bin(unsigned n)``{   string ans;``    ``while``(n > 0){``        ``ans = (to_string(n&1)) + ans;``        ``n >>= 1;``    ``}``    ` `    ``return` `ans;``}` `// This function returns true if binary``// representation of x is palindrome``bool` `checkPalindrome( unsigned ``int` `n){``    ``string s1 = bin(n);``    ``string s2 = s1;``    ` `    ``// reversing the string 1``    ``reverse(s2.begin(), s2.end());``    ` `    ``return` `s1 == s2;``}` `// Driver code``int` `main() {``    ``unsigned ``int` `x = 1 << 15 + 1 << 16;``    ``cout << checkPalindrome(x) << endl;``    ``x = 10;``    ``cout << checkPalindrome(x) << endl;``    ``return` `0;``}`

## Java

 `// Java program to check if binary representation``// of a number is palindrome``class` `GFG``{``  ` `  ``// This function return the binary form of integer in string format``  ``static` `String bin(``int` `n)``  ``{  ``    ``String ans = ``""``;``    ``while``(n > ``0``){``      ``ans = (Integer.toString(n&``1``)) + ans;``      ``n >>= ``1``;``    ``}` `    ``return` `ans;``  ``}` `  ``// This function returns true if binary``  ``// representation of x is palindrome``  ``static` `int` `checkPalindrome(``int` `n){``    ``String s1 = bin(n);` `    ``// reversing the string 1``    ``StringBuilder s2 = ``new` `StringBuilder(s1);``    ``s2 = s2.reverse();`  `    ``return` `s1.equals(s2.toString()) ? ``1` `: ``0``;``  ``}` `  ``public` `static` `void` `main(String[] args) {``    ``int` `x = ``9``;``    ``System.out.println(checkPalindrome(x));``    ``x = ``10``;``    ``System.out.println(checkPalindrome(x)); ``  ``}``}` `// This code is contributed by phasing17.`

## Python

 `def` `bin``(n):``    ``ans``=``"";``    ``while` `n > ``0``:``        ``ans ``=` `(``str``(n&``1``)) ``+` `ans;``        ``n >>``=` `1``;``    ``return` `ans;` `def` `checkPalindrome(x):``    ``s1 ``=` `bin``(x)``    ``s2 ``=` `s1[::``-``1``]``    ``return` `1` `if` `s1 ``=``=` `s2 ``else` `0` `# Some test cases....``x ``=` `9``; ``print``(checkPalindrome(x)) ``#  output 1` `x ``=` `10``print``(checkPalindrome(x)) ``# output 0`

## C#

 `// C# program to check if binary representation``// of a number is palindrome``using` `System;` `public` `class` `GFG``{` `  ``// This function returns the binary form of integer in``  ``// string format``  ``static` `string` `bin(``int` `n)``  ``{``    ``string` `ans = ``""``;``    ``while` `(n > 0) {``      ``ans = (Convert.ToString(n & 1)) + ans;``      ``n >>= 1;``    ``}` `    ``return` `ans;``  ``}` `  ``// This function returns true if binary``  ``// representation of x is palindrome``  ``static` `int` `checkPalindrome(``int` `n)``  ``{``    ``string` `s1 = bin(n);` `    ``// reversing the string 1``    ``char``[] charArray = s1.ToCharArray();``    ``Array.Reverse(charArray);``    ``string` `s2 = ``new` `string``(charArray);` `    ``return` `s1.Equals(s2) ? 1 : 0;``  ``}` `  ``// Driver Code``  ``public` `static` `void` `Main(``string``[] args)``  ``{``    ``int` `x = 9;``    ``Console.WriteLine(checkPalindrome(x));``    ``x = 10;``    ``Console.WriteLine(checkPalindrome(x));``  ``}``}` `// This code is contributed by phasing17.`

## Javascript

 `// JavaScript program to check if binary representation``// of a number is palindrome` `// This function return the binary form of integer in string format``function` `bin(n)``{   let ans=``""``;``    ``while``(n > 0){``        ``ans = ((n&1).toString()) + ans;``        ``n >>= 1;``    ``}``    ` `    ``return` `ans;``}` `// This function returns true if binary``// representation of x is palindrome``function` `checkPalindrome(x){``    ``let s1 = bin(x);``    ``// reversing the string s1``    ``let s2 = s1.split(``""``).reverse().join(``""``);``    ``return` `s1 === s2 ? 1 :0;``}` `// Some test case``let x = 1 << 15 + 1 << 16 ;``console.log(checkPalindrome(x));` `x = 10;``console.log(checkPalindrome(x));`

Output

```1
0```

Time Complexity: O(log(x))
Auxiliary Space: O(X)

Method 3: Using builtin method bitset<>

• Convert the given number into its binary form.
• Check if it’s palindrome or not.

Below is the implementation of the above approach:

## C++

 `// C++ program to check if binary representation``// of a number is palindrome``#include ``using` `namespace` `std;` `int` `isPalindrome(``int` `N)``{``    ``// Converting N into binary representation``    ``string s = bitset<32>(N).to_string();``    ``s = s.substr(s.find(``'1'``));` `    ``// Checking if it is palindrome or not``    ``int` `i = 0, j = s.size() - 1;``    ``while` `(i < j) {``        ``if` `(s[i] != s[j])``            ``return` `false``;``        ``i++;``        ``j--;``    ``}``    ``return` `true``;``}` `// Driver code``int` `main()``{``    ``int` `x = 16;``    ``cout << isPalindrome(x) << endl;``    ``x = 17;``    ``cout << isPalindrome(x) << endl;``    ``return` `0;``}` `// This code is contributed by hkdass001`

## Java

 `// Java code for the above approach``import` `java.io.*;` `class` `Main {``  ``public` `static` `boolean` `isPalindrome(``int` `N)``  ``{``    ` `    ``// Converting N into binary representation``    ``String s = Integer.toBinaryString(N);``    ` `    ``// Checking if it is palindrome or not``    ``int` `i = ``0``, j = s.length() - ``1``;``    ``while` `(i < j) {``      ``if` `(s.charAt(i) != s.charAt(j)) {``        ``return` `false``;``      ``}``      ``i++;``      ``j--;``    ``}``    ``return` `true``;``  ``}` `  ``public` `static` `void` `main(String[] args) {``    ``int` `x = ``16``;``    ``System.out.println(isPalindrome(x));``    ``x = ``17``;``    ``System.out.println(isPalindrome(x));``  ``}``}` `// This code is contributed by lokeshpotta20.`

## Python3

 `# Python program to check if binary representation``# of a number is palindrome``import` `math` `def` `isPalindrome(N):``    ``# Converting N into binary representation``    ``s ``=` `bin``(N)[``2``:] ``    ``s ``=` `s[s.index(``'1'``):]   ``    ``# Checking if it is palindrome or not``    ``i ``=` `0``;``    ``j ``=` `len``(s) ``-` `1``;``    ``while` `(i < j):``        ``if` `(s[i] !``=` `s[j]):``            ``return` `0``;``        ``i``+``=``1``;``        ``j``-``=``1``;``    ``return` `1``;` `# Driver code``x ``=` `16``;``print``(isPalindrome(x));``x ``=` `17``;``print``(isPalindrome(x));`

## C#

 `// C# program to check if binary representation``// of a number is palindrome` `using` `System;``using` `System.Linq;``using` `System.Collections.Generic;` `class` `GFG``{` `    ``static` `int` `isPalindrome(``int` `N)``    ``{``        ``// Converting N into binary representation``        ``string` `s = Convert.ToString(N,2);` `        ``// Checking if it is palindrome or not``        ``int` `i = 0, j = s.Length - 1;``        ``while` `(i < j) {``            ``if` `(s[i] != s[j])``                ``return` `0;``            ``i++;``            ``j--;``        ``}``        ``return` `1;``    ``}``    ` `    ``// Driver code``    ``static` `public` `void` `Main()``    ``{``        ``int` `x = 16;``        ``Console.WriteLine(isPalindrome(x));``        ``x = 17;``        ``Console.WriteLine(isPalindrome(x));``    ``}``}`

## Javascript

 `// Javascript program to check if binary representation``// of a number is palindrome``function` `isPalindrome(N)``{``    ``// Converting N into binary representation``    ``const s = N.toString(2);``    ` `    ``// Checking if it is palindrome or not``    ``let i = 0, j = s.length - 1;``    ``while` `(i < j) {``        ``if` `(s[i] != s[j])``            ``return` `0;``        ``i++;``        ``j--;``    ``}``    ``return` `1;``}` `// Driver code``let x = 16;``console.log(isPalindrome(x));``x = 17;``console.log(isPalindrome(x));` `// This code is contributed by agrawalpoojaa976.`

Output

```0
1```

Time Complexity: O(k), where k is the number of bits in the given number X
Auxiliary Space: O(k)

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.

#### Approach#4: using | operator

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.

#### Algorithm

1. Create a copy of the input number and initialize a variable to hold the reversed binary representation.
2. Loop through the bits of the input number and append each bit to the reversed binary representation.
3. Convert the reversed binary representation to an integer and compare it with the original number.
4. If the two numbers are equal, return True, else return False.

## C++

 `#include ``using` `namespace` `std;` `bool` `is_binary_palindrome(``int` `num) {``    ``int` `rev_binary = 0;``    ``int` `copy_num = num;``    ``while` `(copy_num) {``        ``rev_binary = (rev_binary << 1) | (copy_num & 1);``        ``copy_num >>= 1;``    ``}``    ``return` `rev_binary == num;``}` `int` `main() {``    ``int` `num = 9;``    ``cout << is_binary_palindrome(num) << endl;``    ``num = 10;``    ``cout << is_binary_palindrome(num) << endl;``    ``return` `0;``}`

## Java

 `public` `class` `Main {``    ``public` `static` `boolean` `isBinaryPalindrome(``int` `num) {``        ``int` `revBinary = ``0``;``        ``int` `copyNum = num;``        ``while` `(copyNum != ``0``) {``            ``revBinary = (revBinary << ``1``) | (copyNum & ``1``);``            ``copyNum >>= ``1``;``        ``}``        ``return` `revBinary == num;``    ``}` `    ``public` `static` `void` `main(String[] args) {``        ``int` `num = ``9``;``        ``System.out.println(isBinaryPalindrome(num));``        ``num = ``10``;``        ``System.out.println(isBinaryPalindrome(num));``    ``}``}`

## Python3

 `def` `is_binary_palindrome(num):``    ``rev_binary ``=` `0``    ``copy_num ``=` `num``    ``while` `copy_num:``        ``rev_binary ``=` `(rev_binary << ``1``) | (copy_num & ``1``)``        ``copy_num >>``=` `1``    ``return` `rev_binary ``=``=` `num` `num``=``9``print``(is_binary_palindrome(num))``num``=``10``print``(is_binary_palindrome(num))`

Output

```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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