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1024 (number)
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1024 (number) : ウィキペディア英語版
1024 (number)

1024 is the natural number following 1023 and preceding 1025.
1024 is a power of two: 2^ (2 to the 10th power).〔Bryan Bunch, ''The Kingdom of Infinite Number''. New York: W. H. Freeman & Company (2000): 170〕
It is the lowest power of two requiring four decimal digits, and the lowest power of two containing the digit 0 in its decimal representation (excluding any leading zeroes).
It is also the square of 32: 32^.
1024 is the smallest number with ''exactly'' 11 divisors (but note that there are smaller numbers with more than 11 divisors; e.g., 60 has 12 divisors) .
== Approximation to 1000 ==

The neat coincidence that 210 is nearly equal to 103 provides the basis of a technique of estimating larger powers of 2 in decimal notation. Using 210a+b ≈ 2b103a is fairly accurate for exponents up to about 100. For exponents up to 300, 3a continues to be a good estimate of the number of digits.
For example, 253 ≈ 8×1015. The actual value is closer to 9×1015.
In the case of larger exponents the relationship becomes increasingly more inaccurate with errors exceeding an order of magnitude for a \geq 97, for example:
:\begin
\frac}
&= \exp \left( \ln \left( \frac} \right) \right) \\
&= \exp \left( \ln \left( 2^\right) - \ln\left(10^\right)\right)\\
&\approx \exp\left(693.147-690.776\right)\\
&\approx \exp\left(2.372\right)\\
&\approx 10.72
\end
In measuring bytes, 1024 is often used in place of 1000 as the quotients of the units byte, kilobyte, megabyte, etc. In 1999, the IEC coined the term kibibyte for multiples of 1024, with kilobyte being used for multiples of 1000. However, this convention was never widely adopted.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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