Power of two

A power of two is any of the powers of the number two; in other words, two times itself a certain number of times.

Because two is the basis of the binary system, powers of two are useful for measuring computer memory. For instance, a byte is eight (2³) bits, and a kilobyte is 1,024 (2¹⁰) bytes.

Powers of two and numbers one less than powers of two (counting starting from zero) show up commonly in computers and video games because of the programming. For instance, in The Legend of Zelda one can only hold 255 coins at one time, 16-color and 256-color schemes are used by computer monitors, and 65,536 shows up in several places.

A prime number that is one less than a power of two is called a Mersenne prime. For example, the prime number 31 is a Mersenne prime because it is 1 less than 32 (2⁵).

Powers of two:

• 2⁰ = 1
• 2¹ = 2
• 2² = 4
• 2³ = 8
• 2⁴ = 16
• 2⁵ = 32
• 2⁶ = 64
• 2⁷ = 128
• 2⁸ = 256
• 2⁹ = 512
• 2¹⁰ = 1,024
• 2¹¹ = 2,048
• 2¹² = 4,096
• 2¹³ = 8,192
• 2¹⁴ = 16,384
• 2¹⁵ = 32,768
• 2¹⁶ = 65,536
• 2¹⁷ = 131,072
• 2¹⁸ = 262,144
• 2¹⁹ = 524,288
• 2²⁰ = 1,048,576
• 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
• 2³¹ = 2,147,483,648
• 2³² = 4,294,967,296
• 2³³ = 8,589,934,592
• 2³⁴ = 17,179,869,184
• 2³⁵ = 34,359,738,368
• 2³⁶ = 68,719,476,736
• 2³⁷ = 137,438,953,472
• 2³⁸ = 274,877,906,944
• 2³⁹ = 549,755,813,888
• 2⁴⁰ = 1,099,511,627,776
• 2⁴¹ = 2,199,023,255,552
• 2⁴² = 4,398,046,511,104
• 2⁴³ = 8,796,093,022,208
• 2⁴⁴ = 17,592,186,044,416
• 2⁴⁵ = 35,184,372,088,832
• 2⁴⁶ = 70,368,744,177,664
• 2⁴⁷ = 140,737,488,355,328
• 2⁴⁸ = 281,474,976,710,656
• 2⁴⁹ = 562,949,953,421,312
• 2⁵⁰ = 1,125,899,906,842,624
• 2⁵¹ = 2,251,799,813,685,248