What is 2 to the power of 10?

2^10 = 1,024. This is why computer capacities use 1,024 rather than 1,000: a kibibyte is 1,024 bytes, and each next unit multiplies by another 2^10.

What is 2 to the power of 32?

2^32 = 4,294,967,296. A 32-bit system can represent about 4.29 billion distinct values, which is why 32-bit computers are limited to roughly 4 GiB of directly addressable memory.

What is the largest 64-bit number?

An unsigned 64-bit integer tops out at 2^64 - 1 = 18,446,744,073,709,551,615 - about 18.4 quintillion.

Powers of 2 Table — 2⁰ to 2⁶⁴ with Exact Values

Why these numbers rule computing: every bit doubles the number of values a computer can represent, so memory sizes, address spaces, and file sizes all march up the powers of 2. That’s why a “kilobyte” of RAM is really 2¹⁰ = 1,024 bytes, and why 32-bit systems max out at 2³² = 4,294,967,296 addresses.

Power	Exact value	≈ Scientific	In computing
2⁰	1
2¹	2
2²	4
2³	8
2⁴	16
2⁵	32
2⁶	64
2⁷	128
2⁸	256		values in 1 byte
2⁹	512
2¹⁰	1,024		1 KiB (kibibyte)
2¹¹	2,048
2¹²	4,096
2¹³	8,192
2¹⁴	16,384
2¹⁵	32,768
2¹⁶	65,536		values in 2 bytes / 64K
2¹⁷	131,072
2¹⁸	262,144
2¹⁹	524,288
2²⁰	1,048,576		1 MiB (mebibyte)
2²¹	2,097,152
2²²	4,194,304
2²³	8,388,608
2²⁴	16,777,216
2²⁵	33,554,432
2²⁶	67,108,864
2²⁷	134,217,728
2²⁸	268,435,456
2²⁹	536,870,912
2³⁰	1,073,741,824	1.07 × 10⁹	1 GiB (gibibyte)
2³¹	2,147,483,648	2.15 × 10⁹
2³²	4,294,967,296	4.29 × 10⁹	values in 4 bytes / IPv4 space
2³³	8,589,934,592	8.59 × 10⁹
2³⁴	17,179,869,184	1.72 × 10¹⁰
2³⁵	34,359,738,368	3.44 × 10¹⁰
2³⁶	68,719,476,736	6.87 × 10¹⁰
2³⁷	137,438,953,472	1.37 × 10¹¹
2³⁸	274,877,906,944	2.75 × 10¹¹
2³⁹	549,755,813,888	5.50 × 10¹¹
2⁴⁰	1,099,511,627,776	1.10 × 10¹²	1 TiB (tebibyte)
2⁴¹	2,199,023,255,552	2.20 × 10¹²
2⁴²	4,398,046,511,104	4.40 × 10¹²
2⁴³	8,796,093,022,208	8.80 × 10¹²
2⁴⁴	17,592,186,044,416	1.76 × 10¹³
2⁴⁵	35,184,372,088,832	3.52 × 10¹³
2⁴⁶	70,368,744,177,664	7.04 × 10¹³
2⁴⁷	140,737,488,355,328	1.41 × 10¹⁴
2⁴⁸	281,474,976,710,656	2.81 × 10¹⁴
2⁴⁹	562,949,953,421,312	5.63 × 10¹⁴
2⁵⁰	1,125,899,906,842,624	1.13 × 10¹⁵	1 PiB (pebibyte)
2⁵¹	2,251,799,813,685,248	2.25 × 10¹⁵
2⁵²	4,503,599,627,370,496	4.50 × 10¹⁵
2⁵³	9,007,199,254,740,992	9.01 × 10¹⁵
2⁵⁴	18,014,398,509,481,984	1.80 × 10¹⁶
2⁵⁵	36,028,797,018,963,968	3.60 × 10¹⁶
2⁵⁶	72,057,594,037,927,936	7.21 × 10¹⁶
2⁵⁷	144,115,188,075,855,872	1.44 × 10¹⁷
2⁵⁸	288,230,376,151,711,744	2.88 × 10¹⁷
2⁵⁹	576,460,752,303,423,488	5.76 × 10¹⁷
2⁶⁰	1,152,921,504,606,846,976	1.15 × 10¹⁸	1 EiB (exbibyte)
2⁶¹	2,305,843,009,213,693,952	2.31 × 10¹⁸
2⁶²	4,611,686,018,427,387,904	4.61 × 10¹⁸
2⁶³	9,223,372,036,854,775,808	9.22 × 10¹⁸
2⁶⁴	18,446,744,073,709,551,616	1.84 × 10¹⁹	values in 8 bytes

Negative powers of 2

Power	Fraction	Decimal
2⁻¹	1/2	0.5
2⁻²	1/4	0.25
2⁻³	1/8	0.125
2⁻⁴	1/16	0.0625
2⁻⁵	1/32	0.03125
2⁻⁶	1/64	0.015625
2⁻⁷	1/128	0.0078125
2⁻⁸	1/256	0.00390625
2⁻⁹	1/512	0.001953125
2⁻¹⁰	1/1,024	0.0009765625

Need a power that isn’t here — 2¹⁰⁰, 2¹⁰⁰⁰, or a fractional one like 2^1/3? The exponent calculator returns exact values up to 100,000 digits. The rules for combining powers are on the cheat sheet, and the same doubling math drives money too — see the compound growth table.

Did you know?

The missing gigabytes. A “1 TB” drive shows up as ~931 GB because makers count 10¹² bytes while your computer counts in 2³⁰ chunks — the same drive, two different definitions.
Twenty questions, a million answers. Because 2²⁰ > 1,000,000, twenty yes/no questions can pin down any number from 1 to a million — the power behind binary search.
The year-2038 problem. Old systems count seconds in a 32-bit number, which overflows at 2³¹ — exactly on January 19, 2038. It’s Y2K’s binary sequel, and engineers are patching it now.
An internet for every sand grain. IPv6 has 2¹²⁸ addresses — enough to give every grain of sand on Earth about 45 billion billion addresses of its own.
Why CD audio sounds smooth. 16-bit sound divides loudness into 2¹⁶ = 65,536 steps — fine enough that your ear can’t hear the staircase.
The Pac-Man kill screen. Pac-Man’s level counter was one byte, so level 256 overflows and shatters the screen into garbage — one of gaming’s most famous bugs is a power of 2.
Bitcoin’s haystack. A SHA-256 hash has 2²⁵⁶ ≈ 10⁷⁷ possibilities — within a few zeros of the number of atoms in the observable universe.
Why brackets have 64 teams. Knockout tournaments love powers of 2: 64 teams resolve in exactly 6 rounds, because 2⁶ = 64 — no byes, no leftovers.

Powers of 2

Negative powers of 2

Sources & Further Reading