1024 (number)

1024 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 thumb|The number 1024 in a treatise on binary numbers by Leibniz (1697) 1024 is the natural number following 1023 and preceding 1025. 1024 is a power of two: 210 (2 to the tenth power)Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 170 and a power of four: 45 (four to the fifth power). It is the nearest power of two from decimal 1000 and senary 100006 (decimal 1296). It is the 64th quarter square.A002620 floor(n/2)*ceiling(n/2). Equivalently, a(n) = floor(n^2/4). 2024-01-21 Denis Roegel. A reconstruction of Bürger's table of quarter-squares (1817). https://inria.hal.science/hal-00880832/document Research Report 2013 HAL Lyons 18 202132792 It is the smallest four-digit perfect square: 1024 = 322. 1024 is the smallest number with exactly 11 divisors (but there are smaller numbers with more than 11 divisors; e.g., 60 has 12 divisors) A005179. 1024 is a Friedman number. Enumeration of groups The number of groups of order 1024 is 49 487 367 289, up to isomorphism.Burrell David On the number of groups of order 1024 Communications in Algebra 2021-12-08 50 6 2408–2410 10.1080/00927872.2021.2006680 244772374 4413840 https://www.tandfonline.com/doi/full/10.1080/00927872.2021.2006680 subscription An earlier calculation gave this number as 49 487 365 422,http://www.icm.tu-bs.de/ag_algebra/software/small/number.html Numbers of isomorphism types of finite groups of given order www.icm.tu-bs.de https://web.archive.org/web/20190725032846/http://www.icm.tu-bs.de/ag_algebra/software/small/number.html en 2017-04-05 2019-07-25Besche Hans Ulrich Eick Bettina O'Brien E. A. A millennium project: constructing small groups 1935567 2002 International Journal of Algebra and Computation 12 5 623–644 10.1142/S0218196702001115 31716675 but in 2021 this was shown to be in error. This count is more than 99% of all the isomorphism classes of groups of order less than 2000.Paolo Aluffi Paolo Aluffi Algebra: Chapter 0 Algebra: Chapter 0 2009 American Mathematical Society 9780821847817 Approximation to 1000 Binary prefix 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(or 2a≈2a mod 1010floor(a/10) if "a" stands for the whole power) 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 inaccurate, with errors exceeding an order of magnitude for a ≥ 97. For example: 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. Special use in computers In binary notation, 1024 is represented as 10000000000, making it a simple round number occurring frequently in computer applications. 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 or kibibytes. In the Rich Text Format (RTF), 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. 1024×768 pixels and 1280×1024 pixels are common standards of display resolution. 1024 is the lowest non-system and non-reserved port number in TCP/IP networking. Ports above this number can usually be opened for listening by non-superusers. See also Powers of 1024 References 10 Category:Integers