Checking if a Number is a Power of 2

The Power-of-2 Check

A positive integer is a power of 2 if and only if it has exactly one bit set in its binary representation. The classic one-liner test is:

function isPowerOf2(n) {
  return n > 0 && (n & (n - 1)) === 0;
}

Why It Works

A power of 2 in binary is a single 1 followed by zeros:

  1   = 00000001
  2   = 00000010
  4   = 00000100
  8   = 00001000
 16   = 00010000

Subtracting 1 flips the lowest set bit and all bits below it:

  8     = 00001000
  8 - 1 = 00000111

ANDing these together always produces zero for powers of 2 because there is no overlap:

  00001000
& 00000111
──────────
  00000000

For non-powers of 2, at least one higher bit survives:

  6     = 00000110
  6 - 1 = 00000101
  6 & 5 = 00000100  (not zero!)

Edge Cases

• n = 0: Returns false. 0 is not a power of 2, and the n > 0 check handles this.
• n < 0: Returns false. Negative numbers are not powers of 2.
• n = 1: Returns true. 2^0 = 1.

Related Trick: Next Power of 2

To round up to the next power of 2:

function nextPowerOf2(n) {
  n--;
  n |= n >> 1;
  n |= n >> 2;
  n |= n >> 4;
  n |= n >> 8;
  n |= n >> 16;
  return n + 1;
}

This propagates the highest set bit downward, filling all lower bits with 1, then adds 1.