Power of two

In mathematics, a power of two means a number of the form 2ⁿ where n is an integer, i.e. the result of exponentiation with number two as the base and integer n as the exponent.

In a context where only integers are considered, n is restricted to non-negative values, so we have 1, 2, and 2 multiplied by itself a certain number of times.

Because two is the base of the binary numeral system, powers of two are common in computer science. Written in binary, a power of two always has the form 100…000 or 0.00…001, just like a power of ten in the decimal system.

Expressions and notations

Verbal expressions, mathematical notations, and computer programming expressions using a power operator or function include:

Computer science

Two to the power of n, written as 2ⁿ, is the number of ways the bits in a binary word of length n can be arranged. A word, interpreted as an unsigned integer, can represent values from 0 (000…000) to 2ⁿ − 1 (111…111) inclusively. Corresponding signed integer values can be positive, negative and zero; see signed number representations. Either way, one less than a power of two is often the upper bound of an integer in binary computers. As a consequence, numbers of this form show up frequently in computer software. As an example, a video game running on an 8-bit system might limit the score or the number of items the player can hold to 255—the result of using a byte, which is 8 bits long, to store the number, giving a maximum value of 2⁸ − 1 = 255. For example, in the original Legend of Zelda the main character was limited to carrying 255 rupees (the currency of the game) at any given time, and the video game Pac-Man famously shuts down at level 255.

Power of two (disambiguation)

Power of two or variations may refer to:

Swamp Ophelia

Swamp Ophelia is the fifth studio album by the Indigo Girls, released in 1994.

Track listing

Reception

The Allmusic review noted that "Amy Ray and Emily Saliers continue to hone their signature lush melodies .... The Indigo Girls are no longer afraid to hit upon past relationships and personal emotion. Saliers and Ray's incredible harmonies are most stylish .... [b]ut the duo also move beyond the sweet and tender by dipping into darker realms .... This album is another humanistic effort from the Indigo Girls' deep and indwelling passions and ideas."

Covers

In 2009, Michael Feinstein covered "The Power of Two" in his nightclub act and studio album The Power of Two with Cheyenne Jackson, using the song's title for both the album and act as well. In 2010, Filipino pop rock singer Aiza Seguerra also covered the song. In 2012, Filipino acoustic pop singer Nyoy Volante and his acoustic band, "Rhythmic Circle" also covered the song on the OPM pop compilation album 90's Music Comes Alive.