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1023 (number)

Field	Value
number	1023
divisor	1, 3, 11, 31, 33, 93, 341, 1023

1023 is the natural number following 1022 and preceding 1024.

Mathematics

1023 is a number whose sum of digits is 6, and is a sum of 5 consecutive primes (193, 197, 199, 211 and 223).

It is a sub-perfect power (a perfect power minus 1) specifically 45 - 1 and 210 - 1. The latter of these makes it a Mersenne number, and both of these cause it to be palindromic when converted to bases 2 and 4 (as in both they are a string of 1's).

It is a Stirling number of the second kind, specifically \textstyle \left{{11\atop 2}\right}.

There are 1023 polycubes with 7 cells (when counting reflections as distinct, which is standard).

In other fields

Computing

Floating-point units in computers often run a IEEE 754 64-bit, floating-point excess-1023 format in 11-bit binary. In this format, also called binary64, the exponent of a floating-point number (e.g. 1.009001 E1031) appears as an unsigned binary integer from 0 to 2047, where subtracting 1023 from it gives the actual signed value.

1023 is the number of dimensions or length of messages of an error-correcting Reed-Muller code made of 64 block codes.

Technology

The Global Positioning System (GPS) works on a ten-digit binary counter that runs for 1023 weeks, at which point an integer overflow causes its internal value to roll over to zero again.

1023 being 2^{10}-1, is the maximum number that a 10-bit ADC converter can return when measuring the highest voltage in range.

References

{{OEIS link. A052220
{{OEIS link. A034964
{{OEIS link. A045542
{{OEIS link. A000225
{{OEIS link. A097856
{{OEIS link. A008277
{{OEIS link. A000162
{{OEIS link. A008949

Info: Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

integers

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