Check if binary representation of a number is palindrome in Python

Checking if a number's binary representation is a palindrome involves converting the number to binary and verifying if it reads the same forwards and backwards. Python provides several approaches to accomplish this task.

Understanding the Problem

A binary palindrome reads the same from left to right as from right to left. For example, the number 9 has binary representation "1001", which is a palindrome.

Method 1: Using String Conversion

The simplest approach is to convert the number to binary string and check if it's equal to its reverse −

def is_binary_palindrome_string(n):
    binary_str = bin(n)[2:]  # Remove '0b' prefix
    return binary_str == binary_str[::-1]

# Test with example
n = 9
print(f"Binary of {n}: {bin(n)[2:]}")
print(f"Is palindrome: {is_binary_palindrome_string(n)}")

Binary of 9: 1001
Is palindrome: True

Method 2: Using Binary Reversal

This method reverses the binary representation by manipulating bits directly −

def reverse_binary(num):
    ans = 0
    while num > 0:
        ans = ans << 1  # Left shift (multiply by 2)
        if num & 1 == 1:  # If last bit is 1
            ans = ans ^ 1  # Set last bit of ans to 1
        num = num >> 1  # Right shift (divide by 2)
    return ans

def is_binary_palindrome_bitwise(n):
    rev = reverse_binary(n)
    return n == rev

# Test with multiple examples
test_numbers = [9, 5, 17, 21]
for num in test_numbers:
    result = is_binary_palindrome_bitwise(num)
    print(f"Number: {num}, Binary: {bin(num)[2:]}, Palindrome: {result}")

Number: 9, Binary: 1001, Palindrome: True
Number: 5, Binary: 101, Palindrome: True
Number: 17, Binary: 10001, Palindrome: True
Number: 21, Binary: 10101, Palindrome: True

How the Binary Reversal Works

The bitwise method works by:

• Starting with ans = 0
• For each bit in the original number (from right to left):
• Left−shift ans to make room for the next bit
• If the current bit is 1, XOR ans with 1 to set the last bit
• Right−shift the original number to process the next bit

Method 3: Using Two Pointers Approach

Convert to binary string and use two pointers to check palindrome −

def is_binary_palindrome_two_pointers(n):
    binary_str = bin(n)[2:]  # Remove '0b' prefix
    left, right = 0, len(binary_str) - 1
    
    while left < right:
        if binary_str[left] != binary_str[right]:
            return False
        left += 1
        right -= 1
    
    return True

# Test the function
n = 9
print(f"Number: {n}")
print(f"Binary: {bin(n)[2:]}")
print(f"Is palindrome: {is_binary_palindrome_two_pointers(n)}")

Number: 9
Binary: 1001
Is palindrome: True

Comparison

Conclusion

The string conversion method is the most readable and straightforward approach. The binary reversal method is more memory−efficient but requires understanding of bitwise operations. Choose based on your specific requirements for readability versus memory efficiency.