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| {{infobox number
| | Hi there, I am Yoshiko Villareal but I by no means really liked that name. Kansas is our beginning location and my parents reside nearby. The factor she adores most is to play handball but she can't make it her occupation. Interviewing is what she does.<br><br>My web page - [http://Noblesse.ciado.de/index.php?mod=users&action=view&id=9201 Noblesse.ciado.de] |
| | number = 1024
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| | divisor = 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024
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| | unicode =
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| | greek prefix =
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| | latin prefix =
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| }}
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| '''1024''' is the [[natural number]] following [[1023 (number)|1023]] and preceding [[1025 (number)|1025]].
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| 1024 is a [[power of two]]: <math>2^{10}</math> (2 to the 10th power).<ref>Bryan Bunch, ''The Kingdom of Infinite Number''. New York: W. H. Freeman & Company (2000): 170</ref>
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| 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 zero]]es).
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| It is also the [[square (algebra)|square]] of [[32 (number)|32]]: <math>32^{2}</math>.
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| 1024 is the smallest number with ''exactly'' 11 [[divisor]]s (but note that there are smaller numbers with more than 11 divisors; e.g., [[60 (number)|60]] has 12 divisors {{OEIS|A005179}}.
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| == Approximation to 1000 ==
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| {{see also|Binary prefix}}
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| The neat coincidence that 2<sup>10</sup> is nearly equal to [[1000 (number)|10<sup>3</sup>]] provides the basis of a technique of estimating larger powers of 2 in decimal notation. Using 2<sup>10a+b</sup> ≈ 2<sup>b</sup>10<sup>3a</sup> 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.
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| For example, 2<sup>53</sup> ≈ 8×10<sup>15</sup>. The actual value is closer to 9×10<sup>15</sup>.
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| In the case of larger exponents the relationship becomes increasingly more inaccurate with errors exceeding an order of magnitude for <math>a \geq 97</math>, for example:
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| :<math>\begin{align}
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| \frac{2^{1000}}{10^{300}}
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| &= \exp \left( \ln \left( \frac{2^{1000}}{10^{300}} \right) \right) \\
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| &= \exp \left( \ln \left( 2^{1000}\right) - \ln\left(10^{300}\right)\right)\\ | |
| &\approx \exp\left(693.147-690.776\right)\\ | |
| &\approx \exp\left(2.372\right)\\
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| &\approx 10.72
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| \end{align}</math>
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| In measuring [[byte]]s, 1024 is often used in place of 1000 as the quotients of the units [[byte]], [[kilobyte]], [[megabyte]], etc. In 1999, the [[International Electrotechnical Commission|IEC]] coined the term [[kibibyte]] for multiples of 1024, with kilobyte being used for multiples of 1000. As of 2011, this convention has not been widely adopted.
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| == Special use in computers ==
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| In binary notation, 1024 is represented as 10000000000, making it a simple [[round number]] occurring frequently in computer applications.
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| 1024 is the maximum number of computer memory addresses that can be referenced with ten binary switches. This is the origin of the organization of computer memory into 1024-byte chunks ([[Jim Brown (computer scientist)|James Brown]] Method){{citation needed|date=January 2010}} or kilobytes.
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| In the [[Rich Text Format]], language code 1024 indicates the text is not in any language and should be skipped over when proofing. Most used languages codes in RTF are integers slightly over 1024.
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| 1024×[[768 (number)|768]] pixels and [[1280 (number)|1280]]×1024 pixels are common [[Display resolution#Current standards|standards of display resolution]].
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| == References ==
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| {{Reflist}}<!--added above categories/infobox footers by script-assisted edit-->
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| [[Category:Integers|199e03 1024]]
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Hi there, I am Yoshiko Villareal but I by no means really liked that name. Kansas is our beginning location and my parents reside nearby. The factor she adores most is to play handball but she can't make it her occupation. Interviewing is what she does.
My web page - Noblesse.ciado.de