Convert Number to Power of Two

The classic bit trick: n & (n - 1) === 0, valid for positive integers. A power of 2 has exactly one bit set; subtracting 1 flips that bit and sets all lower bits, so AND-ing gives zero. This tool uses that check internally (on BigInt) instead of the floating-point log2(n) === floor(log2(n)) which is unreliable for large numbers.

IEC 80000-13 defines unambiguous binary prefixes (kibi = 2¹⁰ = 1,024; mebi = 2²⁰ = 1,048,576; gibi = 2³⁰; tebi = 2⁴⁰; etc.) to distinguish them from SI decimal prefixes (kilo = 10³ = 1,000). So 1 KiB = 1024 bytes; 1 kB = 1000 bytes. Storage vendors usually advertise in decimal kB while OSes report in binary KiB – the source of the famous “my 1 TB drive shows 931 GB” confusion.

Bit width = how many bits to store the unsigned magnitude of n. For 100 it’s 7 bits because 2⁷ = 128 just exceeds 100. Practically: it’s the size of the smallest integer type that can hold the value – uint7 (no such type, but uint8 = 1 byte covers it). For 1024 the bit width is 11 (not 10) because you need a leading 1 bit at position 10. This matters for bit-field design and storage estimation.

That’s Number.MAX_SAFE_INTEGER – the largest integer where every smaller integer is exactly representable in IEEE-754 double precision. Beyond 2^53, integer arithmetic loses precision (e.g., 2^53 + 1 === 2^53 in regular Number math). For analysis of larger integers, switch to BigInt – which is what this tool does for integer-valued input.

How many times your number is above the nearest lower power of 2. For 100: 100 / 64 = 1.5625, so the ratio is 1.5625×. For 1024 exactly: ratio is 1.0× (it IS the lower power). For 2047 (one less than 2^11): ratio is 31.98× the lower power 2^6 = 64? No – ratio is from THE LOWER ACTUAL POWER, which would be 2^10 = 1024 → ratio 1.998×. Useful for understanding how close you are to the next allocation jump.

Pick Power → Number mode and enter 10. Result: 1024, BigInt-exact, binary 10000000000, hex 0x400, bit width 11. Negative exponents work too: -3 gives 0.125 (but as floating-point, since BigInt only handles integers).

log₂(0) is −∞ and log₂(negative) is complex. Powers of 2 are conventionally defined for positive values. If you want the magnitude of −500, just enter 500 – same result. For zero, “the smallest power of 2 ≥ 0” is 1 (= 2⁰), but the floor of log₂(0) is undefined; we error out to avoid ambiguity.

Yes – 2^256 in binary is 257 characters. For massive inputs the binary row might wrap multiple lines in the UI but the underlying string is exact. If you Copy or Download, the full untruncated string goes to the clipboard / file. Useful for crypto-key sizing or hash-width estimation.

No. All BigInt arithmetic, bit-trick checks, and string formatting happen in your browser. Open DevTools → Network and confirm zero requests fire after the page loads. Safe for sizing memory in proprietary systems or estimating ASIC bit budgets.

Yes. Total bundle is under 20 KB. Once loaded, disconnect and keep using – useful for embedded-systems work or competitive-programming practice where powers of 2 come up constantly.