Binary Powers Table
| Power | Decimal | What it marks |
|---|---|---|
| 21 | 2 | a bit: 0 or 1 |
| 23 | 8 | values in 3 bits - one octal digit |
| 24 | 16 | a nibble: one hex digit |
| 27 | 128 | printable 7-bit ASCII characters |
| 28 | 256 | values in one byte |
| 210 | 1024 | the KiB - 1024, not 1000 |
| 216 | 65536 | uint16: network ports, color channels |
| 220 | 1048576 | the MiB |
| 230 | 1073741824 | the GiB |
| 232 | 4294967296 | uint32 range - the 4 GiB 32-bit memory wall |
| 240 | 1099511627776 | the TiB |
| 248 | 281474976710656 | MAC address space |
| 253 | 9007199254740992 | beyond 2⁵³ − 1, JavaScript numbers stop being exact |
| 264 | 18446744073709551616 | uint64 range: 2⁶⁴ values |
Computing runs on powers of two: a byte holds 2⁸ values, a 32-bit machine hits a 4 GiB wall, JavaScript numbers go exact only to 2⁵³ − 1. This table walks the important ones with what each one marks - and the calculator computes 2ⁿ exactly with BigInt, where ordinary numbers silently start rounding.
The same powers explain the storage fight: drive makers count in thousands (10¹²), operating systems in 2³⁰ - so your 1 TB drive shows 931 GiB and nobody is lying.
How to use
- Type any exponent 0-1000 for 2ⁿ in full decimal - exact, comma-grouped, no rounding.
- Read the table’s third column for why each power matters: hex digits, ASCII, memory walls, address spaces.
- Check the bits note under the result: it tells you whether your exponent still fits a plain number or needs BigInt.
Frequently asked questions
Why does JavaScript stop being exact at 2⁵³?
Numbers are 64-bit floats: 52 explicit mantissa bits plus one hidden. Past 2⁵³ − 1 = 9,007,199,254,740,991 there are more integers than mantissa patterns, so 2⁵³ and 2⁵³ + 1 share a representation. BigInt escapes the limit - the calculator uses it.
Why does my 1 TB drive show 931 GiB?
Terabyte means 10¹² bytes; the drive is honest. The OS divides by 2⁴⁰ = 1,099,511,627,776 to show GiB: 10¹² ÷ 2⁴⁰ ≈ 909.5 - and 931 for a true 10¹²-byte drive depends on the exact count. Same bytes, two rulers; the table’s 2⁴⁰ row is the exchange rate.
What is special about 2³²?
A 32-bit register can address 2³² byte slots - 4,294,967,296 bytes, the famous 4 GiB ceiling that made 32-bit machines cap out no matter how much RAM you installed. The same count is why IPv4 has "only" about 4.3 billion addresses.
How far can the calculator go?
To 2¹⁰⁰⁰ - a 302-digit number - because it multiplies with BigInt instead of floats. Try 2⁵³ in it: exact. A spreadsheet will show you a rounded 9.0072E+15 and hide the loss.