2¹⁰ = 1,024, which is why a kibibyte is 1,024 bytes, and 2³² = 4,294,967,296, the number of IPv4 addresses.
| n | 2ⁿ | Common use |
|---|---|---|
| 0 | 1 | |
| 1 | 2 | |
| 2 | 4 | |
| 3 | 8 | |
| 4 | 16 | |
| 5 | 32 | |
| 6 | 64 | |
| 7 | 128 | |
| 8 | 256 | Values in one byte |
| 9 | 512 | |
| 10 | 1,024 | 1 KiB (kibibyte) |
| 11 | 2,048 | |
| 12 | 4,096 | |
| 13 | 8,192 | |
| 14 | 16,384 | |
| 15 | 32,768 | |
| 16 | 65,536 | Values in 16 bits |
| 17 | 131,072 | |
| 18 | 262,144 | |
| 19 | 524,288 | |
| 20 | 1,048,576 | 1 MiB (mebibyte) |
| 21 | 2,097,152 | |
| 22 | 4,194,304 | |
| 23 | 8,388,608 | |
| 24 | 16,777,216 | 16.7 million colours (24-bit) |
| 25 | 33,554,432 | |
| 26 | 67,108,864 | |
| 27 | 134,217,728 | |
| 28 | 268,435,456 | |
| 29 | 536,870,912 | |
| 30 | 1,073,741,824 | 1 GiB (gibibyte) |
| 31 | 2,147,483,648 | |
| 32 | 4,294,967,296 | IPv4 addresses, 32-bit values |
| 33 | 8,589,934,592 | |
| 34 | 17,179,869,184 | |
| 35 | 34,359,738,368 | |
| 36 | 68,719,476,736 | |
| 37 | 137,438,953,472 | |
| 38 | 274,877,906,944 | |
| 39 | 549,755,813,888 | |
| 40 | 1,099,511,627,776 | 1 TiB (tebibyte) |
| 41 | 2,199,023,255,552 | |
| 42 | 4,398,046,511,104 | |
| 43 | 8,796,093,022,208 | |
| 44 | 17,592,186,044,416 | |
| 45 | 35,184,372,088,832 | |
| 46 | 70,368,744,177,664 | |
| 47 | 140,737,488,355,328 | |
| 48 | 281,474,976,710,656 | |
| 49 | 562,949,953,421,312 | |
| 50 | 1,125,899,906,842,624 | 1 PiB (pebibyte) |
| 51 | 2,251,799,813,685,248 | |
| 52 | 4,503,599,627,370,496 | |
| 53 | 9,007,199,254,740,992 | |
| 54 | 18,014,398,509,481,984 | |
| 55 | 36,028,797,018,963,968 | |
| 56 | 72,057,594,037,927,936 | |
| 57 | 144,115,188,075,855,872 | |
| 58 | 288,230,376,151,711,744 | |
| 59 | 576,460,752,303,423,488 | |
| 60 | 1,152,921,504,606,846,976 | 1 EiB (exbibyte) |
| 61 | 2,305,843,009,213,693,952 | |
| 62 | 4,611,686,018,427,387,904 | |
| 63 | 9,223,372,036,854,775,808 | |
| 64 | 18,446,744,073,709,551,616 | Values in 64 bits |
How it is computed
Each row doubles the one before it: 2ⁿ = 2 × 2ⁿ⁻¹, with 2⁰ = 1. Values are computed with exact integer arithmetic, so even 2⁶⁴ is shown to the last digit.
FAQ
Why is a kilobyte sometimes 1,024 bytes?+
Computer memory is addressed in binary, so 2¹⁰ = 1,024 was the handy size near 1,000. The standard name for 1,024 bytes is kibibyte (KiB); a kilobyte (kB) is 1,000 bytes.
What is the largest value in 64 bits?+
2⁶⁴ − 1 for an unsigned integer, and 2⁶³ − 1 for a signed one, since one bit holds the sign.