Check for Power of two in JavaScript

We need to write a function, isPowerOfTwo(), that takes a positive number and returns a boolean based on whether the number is a power of 2.

For example:

isPowerOfTwo(3)    // false (3 is not a power of 2)
isPowerOfTwo(32)   // true (32 = 2^5)
isPowerOfTwo(2048) // true (2048 = 2^11)
isPowerOfTwo(256)  // true (256 = 2^8)
isPowerOfTwo(22)   // false (22 is not a power of 2)

Method 1: Using Recursive Division

This approach recursively divides the number by 2 until it reaches 1 (power of 2) or becomes odd (not a power of 2):

const isPowerOfTwo = num => {
    if (num === 1) {
        return true;
    }
    if (num % 2 !== 0) {
        return false;
    }
    return isPowerOfTwo(num / 2);
}

console.log(isPowerOfTwo(3));
console.log(isPowerOfTwo(32));
console.log(isPowerOfTwo(2048));
console.log(isPowerOfTwo(256));
console.log(isPowerOfTwo(22));

false
true
true
true
false

Method 2: Using Bitwise AND Operation

A more efficient approach uses the mathematical property that powers of 2 have only one bit set. For any power of 2 n, the expression n & (n-1) equals 0:

const isPowerOfTwoBitwise = num => {
    return num > 0 && (num & (num - 1)) === 0;
}

console.log(isPowerOfTwoBitwise(3));
console.log(isPowerOfTwoBitwise(32));
console.log(isPowerOfTwoBitwise(2048));
console.log(isPowerOfTwoBitwise(256));
console.log(isPowerOfTwoBitwise(22));

false
true
true
true
false

How the Bitwise Method Works

Powers of 2 in binary have exactly one bit set:

8 (2^3):    1000
8-1 = 7:    0111
8 & 7:      0000  ? equals 0

16 (2^4):   10000
16-1 = 15:  01111
16 & 15:    00000  ? equals 0

Comparison

Conclusion

The bitwise method n & (n-1) === 0 is the most efficient way to check powers of 2. It runs in constant time and uses the mathematical property that powers of 2 have exactly one bit set in binary.