Powers of 2 Table — 2⁰ to 2¹⁰⁰, with Binary and Hex
Every power of two from 2⁰ to 2⁶⁴ in decimal, hex and binary — plus 2⁶⁵ to 2¹⁰⁰, negative powers and integer ranges.
No signup, no trackingQuick answer: powers of 2 double at every step — 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 — and the landmarks are 2¹⁰ = 1,024, 2¹⁶ = 65,536, 2²⁰ = 1,048,576, 2³² = 4,294,967,296 and 2⁶⁴ = 18,446,744,073,709,551,616. The table lists every power from 2⁰ to 2⁶⁴ in decimal, hexadecimal and binary, with what each one means in computing, followed by 2⁶⁵ to 2¹⁰⁰, the negative powers, and how many values fit in 8, 16, 32 and 64 bits.
In binary every power of 2 is a 1 followed by n zeros, and in hexadecimal a 1, 2, 4 or 8 followed by zeros — which is why memory sizes, color depths and integer limits are all powers of 2. Every value here is exact, computed with arbitrary-precision integers rather than typed in. To convert any other number between bases, use the number base converter.
Powers of 2 from 2⁰ to 2⁶⁴
| n | 2ⁿ | Hex | Binary | In computing |
|---|---|---|---|---|
| 0 | 1 | 1 | 1 | Any number to the power 0 is 1 |
| 1 | 2 | 2 | 10 | |
| 2 | 4 | 4 | 100 | |
| 3 | 8 | 8 | 1000 | |
| 4 | 16 | 10 | 10000 | Values in a nibble — one hex digit |
| 5 | 32 | 20 | 100000 | |
| 6 | 64 | 40 | 1000000 | |
| 7 | 128 | 80 | 10000000 | ASCII has 2⁷ = 128 characters |
| 8 | 256 | 100 | 100000000 | Values in one byte (0–255) |
| 9 | 512 | 200 | 1000000000 | |
| 10 | 1,024 | 400 | 10000000000 | 1 KiB (kibibyte) — about a thousand |
| 11 | 2,048 | 800 | 100000000000 | |
| 12 | 4,096 | 1000 | 1000000000000 | |
| 13 | 8,192 | 2000 | 10000000000000 | |
| 14 | 16,384 | 4000 | 100000000000000 | |
| 15 | 32,768 | 8000 | 1000000000000000 | |
| 16 | 65,536 | 10000 | 10000000000000000 | Values in 16 bits; TCP/UDP ports run 0–65,535 |
| 17 | 131,072 | 20000 | 1 followed by 17 zeros | |
| 18 | 262,144 | 40000 | 1 followed by 18 zeros | |
| 19 | 524,288 | 80000 | 1 followed by 19 zeros | |
| 20 | 1,048,576 | 100000 | 1 followed by 20 zeros | 1 MiB (mebibyte) — about a million |
| 21 | 2,097,152 | 200000 | 1 followed by 21 zeros | |
| 22 | 4,194,304 | 400000 | 1 followed by 22 zeros | |
| 23 | 8,388,608 | 800000 | 1 followed by 23 zeros | |
| 24 | 16,777,216 | 1000000 | 1 followed by 24 zeros | Colors in 24-bit RGB (16.7 million) |
| 25 | 33,554,432 | 2000000 | 1 followed by 25 zeros | |
| 26 | 67,108,864 | 4000000 | 1 followed by 26 zeros | |
| 27 | 134,217,728 | 8000000 | 1 followed by 27 zeros | |
| 28 | 268,435,456 | 10000000 | 1 followed by 28 zeros | |
| 29 | 536,870,912 | 20000000 | 1 followed by 29 zeros | |
| 30 | 1,073,741,824 | 40000000 | 1 followed by 30 zeros | 1 GiB (gibibyte) — about a billion |
| 31 | 2,147,483,648 | 80000000 | 1 followed by 31 zeros | Signed 32-bit integers stop one below this |
| 32 | 4,294,967,296 | 100000000 | 1 followed by 32 zeros | Values in 32 bits; the IPv4 address space |
| 33 | 8,589,934,592 | 200000000 | 1 followed by 33 zeros | |
| 34 | 17,179,869,184 | 400000000 | 1 followed by 34 zeros | |
| 35 | 34,359,738,368 | 800000000 | 1 followed by 35 zeros | |
| 36 | 68,719,476,736 | 1000000000 | 1 followed by 36 zeros | |
| 37 | 137,438,953,472 | 2000000000 | 1 followed by 37 zeros | |
| 38 | 274,877,906,944 | 4000000000 | 1 followed by 38 zeros | |
| 39 | 549,755,813,888 | 8000000000 | 1 followed by 39 zeros | |
| 40 | 1,099,511,627,776 | 10000000000 | 1 followed by 40 zeros | 1 TiB (tebibyte) |
| 41 | 2,199,023,255,552 | 20000000000 | 1 followed by 41 zeros | |
| 42 | 4,398,046,511,104 | 40000000000 | 1 followed by 42 zeros | |
| 43 | 8,796,093,022,208 | 80000000000 | 1 followed by 43 zeros | |
| 44 | 17,592,186,044,416 | 100000000000 | 1 followed by 44 zeros | |
| 45 | 35,184,372,088,832 | 200000000000 | 1 followed by 45 zeros | |
| 46 | 70,368,744,177,664 | 400000000000 | 1 followed by 46 zeros | |
| 47 | 140,737,488,355,328 | 800000000000 | 1 followed by 47 zeros | |
| 48 | 281,474,976,710,656 | 1000000000000 | 1 followed by 48 zeros | |
| 49 | 562,949,953,421,312 | 2000000000000 | 1 followed by 49 zeros | |
| 50 | 1,125,899,906,842,624 | 4000000000000 | 1 followed by 50 zeros | 1 PiB (pebibyte) |
| 51 | 2,251,799,813,685,248 | 8000000000000 | 1 followed by 51 zeros | |
| 52 | 4,503,599,627,370,496 | 10000000000000 | 1 followed by 52 zeros | |
| 53 | 9,007,199,254,740,992 | 20000000000000 | 1 followed by 53 zeros | JavaScript’s largest exact integer is 2⁵³ − 1 |
| 54 | 18,014,398,509,481,984 | 40000000000000 | 1 followed by 54 zeros | |
| 55 | 36,028,797,018,963,968 | 80000000000000 | 1 followed by 55 zeros | |
| 56 | 72,057,594,037,927,936 | 100000000000000 | 1 followed by 56 zeros | |
| 57 | 144,115,188,075,855,872 | 200000000000000 | 1 followed by 57 zeros | |
| 58 | 288,230,376,151,711,744 | 400000000000000 | 1 followed by 58 zeros | |
| 59 | 576,460,752,303,423,488 | 800000000000000 | 1 followed by 59 zeros | |
| 60 | 1,152,921,504,606,846,976 | 1000000000000000 | 1 followed by 60 zeros | 1 EiB (exbibyte) |
| 61 | 2,305,843,009,213,693,952 | 2000000000000000 | 1 followed by 61 zeros | |
| 62 | 4,611,686,018,427,387,904 | 4000000000000000 | 1 followed by 62 zeros | |
| 63 | 9,223,372,036,854,775,808 | 8000000000000000 | 1 followed by 63 zeros | Signed 64-bit integers stop one below this |
| 64 | 18,446,744,073,709,551,616 | 10000000000000000 | 1 followed by 64 zeros | Values in 64 bits |
Powers of 2 from 2⁶⁵ to 2¹⁰⁰
| n | 2ⁿ |
|---|---|
| 65 | 36,893,488,147,419,103,232 |
| 66 | 73,786,976,294,838,206,464 |
| 67 | 147,573,952,589,676,412,928 |
| 68 | 295,147,905,179,352,825,856 |
| 69 | 590,295,810,358,705,651,712 |
| 70 | 1,180,591,620,717,411,303,424 |
| 71 | 2,361,183,241,434,822,606,848 |
| 72 | 4,722,366,482,869,645,213,696 |
| 73 | 9,444,732,965,739,290,427,392 |
| 74 | 18,889,465,931,478,580,854,784 |
| 75 | 37,778,931,862,957,161,709,568 |
| 76 | 75,557,863,725,914,323,419,136 |
| 77 | 151,115,727,451,828,646,838,272 |
| 78 | 302,231,454,903,657,293,676,544 |
| 79 | 604,462,909,807,314,587,353,088 |
| 80 | 1,208,925,819,614,629,174,706,176 |
| 81 | 2,417,851,639,229,258,349,412,352 |
| 82 | 4,835,703,278,458,516,698,824,704 |
| 83 | 9,671,406,556,917,033,397,649,408 |
| 84 | 19,342,813,113,834,066,795,298,816 |
| 85 | 38,685,626,227,668,133,590,597,632 |
| 86 | 77,371,252,455,336,267,181,195,264 |
| 87 | 154,742,504,910,672,534,362,390,528 |
| 88 | 309,485,009,821,345,068,724,781,056 |
| 89 | 618,970,019,642,690,137,449,562,112 |
| 90 | 1,237,940,039,285,380,274,899,124,224 |
| 91 | 2,475,880,078,570,760,549,798,248,448 |
| 92 | 4,951,760,157,141,521,099,596,496,896 |
| 93 | 9,903,520,314,283,042,199,192,993,792 |
| 94 | 19,807,040,628,566,084,398,385,987,584 |
| 95 | 39,614,081,257,132,168,796,771,975,168 |
| 96 | 79,228,162,514,264,337,593,543,950,336 |
| 97 | 158,456,325,028,528,675,187,087,900,672 |
| 98 | 316,912,650,057,057,350,374,175,801,344 |
| 99 | 633,825,300,114,114,700,748,351,602,688 |
| 100 | 1,267,650,600,228,229,401,496,703,205,376 |
2¹⁰⁰ has 31 digits. A quick way to estimate any large power: 2¹⁰ ≈ 10³, so 2¹⁰⁰ = (2¹⁰)¹⁰ ≈ 10³⁰ — close to the exact 1.27 × 10³⁰.
Negative powers of 2
| n | Fraction | Decimal (exact) |
|---|---|---|
| −1 | 1/2 | 0.5 |
| −2 | 1/4 | 0.25 |
| −3 | 1/8 | 0.125 |
| −4 | 1/16 | 0.0625 |
| −5 | 1/32 | 0.03125 |
| −6 | 1/64 | 0.015625 |
| −7 | 1/128 | 0.0078125 |
| −8 | 1/256 | 0.00390625 |
| −9 | 1/512 | 0.001953125 |
| −10 | 1/1,024 | 0.0009765625 |
| −11 | 1/2,048 | 0.00048828125 |
| −12 | 1/4,096 | 0.000244140625 |
| −13 | 1/8,192 | 0.0001220703125 |
| −14 | 1/16,384 | 0.00006103515625 |
| −15 | 1/32,768 | 0.000030517578125 |
| −16 | 1/65,536 | 0.0000152587890625 |
Every negative power of 2 has a finite decimal, because 2⁻ⁿ = 5ⁿ / 10ⁿ: 2⁻³ = 125 / 1000 = 0.125. That is also why 0.5, 0.25 and 0.125 are exact in binary floating point while 0.1 is not.
How many values fit in n bits
| Bits | Values (2ⁿ) | Unsigned range | Signed range |
|---|---|---|---|
| 8 | 256 | 0 to 255 | −128 to 127 |
| 16 | 65,536 | 0 to 65,535 | −32,768 to 32,767 |
| 32 | 4,294,967,296 | 0 to 4,294,967,295 | −2,147,483,648 to 2,147,483,647 |
| 64 | 18,446,744,073,709,551,616 | 0 to 18,446,744,073,709,551,615 | −9,223,372,036,854,775,808 to 9,223,372,036,854,775,807 |
n bits hold 2ⁿ different values. Unsigned, they run from 0 to 2ⁿ − 1; signed (two’s complement), from −2ⁿ⁻¹ to 2ⁿ⁻¹ − 1 — which is why a signed 32-bit counter overflows just past 2,147,483,647. Handy pattern: from 2¹ on, the last digit cycles 2, 4, 8, 6.
Source: sofritools.com/reference/powers-of-2-table/