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) (sequence A005179 in the OEIS).
The number of groups of order 1024 is 49487365422, which is 99% of all groups of order less than 2000.[2][3]
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.
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.
^Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 170
^. www.icm.tu-bs.de. Archived from the original on 2019-07-25. Retrieved 2017-04-05.
^Besche, Hans Ulrich; Eick, Bettina; O'Brien, E. A. (2002), "A millennium project: constructing small groups", International Journal of Algebra and Computation, 12 (5): 623–644, doi:10.1142/S0218196702001115, MR 1935567, S2CID 31716675
January 12, 2023
1024, number, 1024, natural, number, following, 1023, preceding, 1025, 1023, 1024, 1025, list, numbersintegers, cardinalone, thousand, twenty, fourordinal1024th, thousand, twenty, fourth, factorization210divisors1, 1024greek, numeral, ΑΚΔ, roman, numeralmxxivb. 1024 is the natural number following 1023 and preceding 1025 1023 1024 1025 List of numbersIntegers 0 1k 2k 3k 4k 5k 6k 7k 8k 9k Cardinalone thousand twenty fourOrdinal1024th one thousand twenty fourth Factorization210Divisors1 2 4 8 16 32 64 128 256 512 1024Greek numeral AKD Roman numeralMXXIVBinary100000000002Ternary11012213Senary44246Octal20008Duodecimal71412Hexadecimal40016The number 1024 in a treatise on binary numbers by Leibniz 1697 1024 is a power of two 210 2 to the tenth power 1 It is the nearest power of two from decimal 1000 and senary 100006 decimal 1296 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 sequence A005179 in the OEIS The number of groups of order 1024 is 49487 365 422 which is 99 of all groups of order less than 2000 2 3 Contents 1 Approximation to 1000 2 Special use in computers 3 See also 4 ReferencesApproximation to 1000 EditSee also 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 2 1000 10 300 exp ln 2 1000 10 300 exp ln 2 1000 ln 10 300 exp 693 147 690 776 exp 2 372 10 72 displaystyle begin aligned frac 2 1000 10 300 amp exp left ln left frac 2 1000 10 300 right right amp exp left ln left 2 1000 right ln left 10 300 right right amp approx exp left 693 147 690 776 right amp approx exp left 2 372 right amp approx 10 72 end aligned 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 EditIn 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 See also EditPowers of 1024References Edit Bryan Bunch The Kingdom of Infinite Number New York W H Freeman amp Company 2000 170 Numbers of isomorphism types of finite groups of given order www icm tu bs de Archived from the original on 2019 07 25 Retrieved 2017 04 05 Besche Hans Ulrich Eick Bettina O Brien E A 2002 A millennium project constructing small groups International Journal of Algebra and Computation 12 5 623 644 doi 10 1142 S0218196702001115 MR 1935567 S2CID 31716675 Retrieved from https en wikipedia org w index php title 1024 number amp oldid 1118547664, wikipedia, wiki, book, books, library,
