1023 (number)

{{infobox number

| number = 1023

| divisor = 1, 3, 11, 31, 33, 93, 341, 1023

| unicode =

| greek prefix =

| latin prefix =

}}

1023 is the natural number following 1022 and preceding 1024.

Mathematics

1023 is a number whose sum of digits is 6,{{OEIS link|A052220}} and is a sum of 5 consecutive primes (193, 197, 199, 211 and 223).{{OEIS link|A034964}}

It is a sub-perfect power (a perfect power minus 1) specifically 4^5 - 1 and 2^10 - 1.{{OEIS link|A045542}} The latter of these makes it a Mersenne number,{{OEIS link|A000225}} 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).{{OEIS link|A097856}}

It is a Stirling number of the second kind, specifically $\textstyle \left\{{11\atop 2}\right\}$ .{{OEIS link|A008277}}

There are 1023 polycubes with 7 cells (when counting reflections as distinct, which is standard).{{OEIS link|A000162}}

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.{{OEIS link|A008949}}

=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

Category:Integers