Power of two

A power of two is a number of the form $2 n$ where $n$ is an integer, that is, the result of exponentiation with number two as the base and integer $n$ as the exponent.

Powers of two with non-negative exponents are integers: $20 = 1$ , $21 = 2$ , and $2 n$ is two multiplied by itself $n$ times.^[1]^[2] The first ten powers of 2 for non-negative values of $n$ are:

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ... (sequence A000079 in the OEIS)

By comparison, powers of two with negative exponents are fractions: for a negative integer $n$ , $2 n$ is one half multiplied by itself $n$ times. Thus the first few powers of two where $n$ is negative are ⁠1/2⁠, ⁠1/4⁠, ⁠1/8⁠, ⁠1/16⁠, etc. Sometimes these are called inverse powers of two because each is the multiplicative inverse of a positive power of two.

^ Lipschutz, Seymour (1982). Schaum's Outline of Theory and Problems of Essential Computer Mathematics. New York: McGraw-Hill. p. 3. ISBN 0-07-037990-4.
^ Sewell, Michael J. (1997). Mathematics Masterclasses. Oxford: Oxford University Press. p. 78. ISBN 0-19-851494-8.

[1] Lipschutz, Seymour (1982). Schaum's Outline of Theory and Problems of Essential Computer Mathematics. New York: McGraw-Hill. p. 3. ISBN 0-07-037990-4.

[2] Sewell, Michael J. (1997). Mathematics Masterclasses. Oxford: Oxford University Press. p. 78. ISBN 0-19-851494-8.

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Power of two

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