Python Program to find whether a no is power of two

In this article, we will learn how to check whether a given number is a power of two. A number is a power of two if it can be expressed as 2^n where n is a non-negative integer (e.g., 1, 2, 4, 8, 16, 32...).

Problem statement ? We are given a number, we need to check that the number is a power of two or not.

We can solve this using three approaches as discussed below.

Using Division Method

This approach repeatedly divides the number by 2 until we reach 1 or find that the number is not divisible by 2 ?

# Check if number is power of 2 using division
def is_power_of_two_division(n):
    if n <= 0:
        return False
    while n != 1:
        if n % 2 != 0:
            return False
        n = n // 2
    return True

# Test with different numbers
test_numbers = [1, 2, 4, 8, 16, 98, 64, 100]

for num in test_numbers:
    if is_power_of_two_division(num):
        print(f"{num} is a power of 2")
    else:
        print(f"{num} is not a power of 2")

1 is a power of 2
2 is a power of 2
4 is a power of 2
8 is a power of 2
16 is a power of 2
98 is not a power of 2
64 is a power of 2
100 is not a power of 2

Using Bitwise AND Operation

This approach uses the property that a power of 2 has only one bit set in its binary representation. For any power of 2, n & (n-1) equals 0 ?

# Check if number is power of 2 using bitwise operation
def is_power_of_two_bitwise(n):
    # n must be positive and n & (n-1) should be 0
    return n > 0 and (n & (n - 1)) == 0

# Test with different numbers
test_numbers = [1, 2, 4, 8, 16, 98, 64, 100]

for num in test_numbers:
    if is_power_of_two_bitwise(num):
        print(f"{num} is a power of 2")
    else:
        print(f"{num} is not a power of 2")

1 is a power of 2
2 is a power of 2
4 is a power of 2
8 is a power of 2
16 is a power of 2
98 is not a power of 2
64 is a power of 2
100 is not a power of 2

Using Logarithm Method

This approach calculates log?(n) and checks if the result is an integer ?

import math

# Check if number is power of 2 using logarithm
def is_power_of_two_log(n):
    if n <= 0:
        return False
    
    # Calculate log base 2
    log_result = math.log2(n)
    
    # Check if log result is an integer
    return log_result == int(log_result)

# Test with different numbers
test_numbers = [1, 2, 4, 8, 16, 98, 64, 100]

for num in test_numbers:
    if is_power_of_two_log(num):
        print(f"{num} is a power of 2")
    else:
        print(f"{num} is not a power of 2")

1 is a power of 2
2 is a power of 2
4 is a power of 2
8 is a power of 2
16 is a power of 2
98 is not a power of 2
64 is a power of 2
100 is not a power of 2

Comparison

Conclusion

The bitwise AND method is the most efficient approach with O(1) time complexity. Use the division method for better readability, and the logarithm method when working with mathematical computations.