1024 (number)

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← 1023
1025 →
1024
Cardinal One thousand and twenty-four
Ordinal 1024th
(One thousand and twenty-fourth)
Factorization 210
Divisors 11
Roman numeral MXXIV
Binary 100000000002
Octal 20008
Duodecimal 71412
Hexadecimal 40016

1024 is the natural number following 1023 and preceding 1025.

1024 is a power of two: 210 (2 to the 10th power).1

It is also the square of 32: 322 (32 to the 2nd power).

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 — see the sequence A005179 in OEIS).

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 ≈ 8x1015. The actual value is closer to 9x1015.

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:

\frac{2^{1000}}{10^{300}} \,     = \quad \exp \left( \ln \left( \frac{2^{1000}}{10^{300}} \right) \right) \,    
    = \quad \exp \left( \ln \left( 2^{1000}\right) - \ln\left(10^{300}\right)\right) \,    
    \approx \quad \exp\left(693.147-690.776\right) \,    
    \approx \quad \exp(2.372) \,    
    \approx \quad 10.72 \,    

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. As of 2008, this convention has not been widely adopted.

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 (Steve Brown Method) or kibibytes.

In the Rich Text Format, language code 1024 indicates the text is not in any language and should be skipped over when proofing.

References

  1. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 170


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Wikipedia content modification information:

  • This page was last modified on 7 December 2008, at 22:33.

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