Check if Binary representation is Palindrome in Python

Given a number n, the task is to check whether its binary representation is a palindrome or not. A binary palindrome means that the binary digits of a number read the same backward as forward.

For Example:

Input: n = 9 -> Binary: 1001 -> Output: True
Input: n = 10 -> Binary: 1010 -> Output: False

Let’s explore different ways to check this in Python.

Using Bitwise Operations (Without String Conversion)

This method checks palindrome property purely with bit manipulation. It extracts bits from both ends using shifting and masking. Avoids any string operation.

True

Explanation:

• n.bit_length() gives the number of bits in the binary representation.
• The loop checks bits from both ends using bit shifts and masks (& 1).
• If mismatched bits are found, it’s not a palindrome.

Using String Reversal

This method converts the number into its binary form, removes the '0b' prefix, and checks if the binary string is the same when reversed. It’s short, efficient, and uses Python’s built-in slicing.

True

Explanation:

• bin(n) converts a number into its binary string (e.g., 9 -> '0b1001').
• [2:] removes the '0b' prefix.
• binary[::-1] reverses the binary string.

Using Iteration (Two-pointer Approach)

Instead of reversing the string, this method compares characters from both ends moving toward the center. It avoids creating an extra reversed copy, making it slightly more memory-efficient.

True

Explanation:

• The binary string is created using bin(n)[2:].
• left and right pointers start at opposite ends of the string.
• Each character is compared; if any mismatch occurs, the loop breaks.
• If all pairs match, it confirms the binary representation is a palindrome.

Using Manual Reverse Construction

This method builds the reverse binary manually using bit manipulation and then compares it to the original. It’s slower than the direct check but useful for understanding binary manipulation.

True

Explanation:

• The loop reconstructs the reversed binary bit-by-bit using shifting (<<, >>) and masking (& 1).
• rev becomes the reversed binary of original.
• Comparison determines if the binary representation is symmetric.