1023 (number)

1023 is the natural number following 1022 and preceding 1024.

← 1022 1023 1024 →
List of numbers Integers ← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →
Cardinal	one thousand twenty-three
Ordinal	1023rd (one thousand twenty-third)
Factorization	3 × 11 × 31
Divisors	1, 3, 11, 31, 33, 93, 341, 1023
Greek numeral	,ΑΚΓ´
Roman numeral	MXXIII, mxxiii
Binary	11111111112
Ternary	11012203
Senary	44236
Octal	17778
Duodecimal	71312
Hexadecimal	3FF16

Mathematics

1023 is a number whose sum of digits is 6,^[1] and is a sum of 5 consecutive primes (193, 197, 199, 211 and 223).^[2]

It is a sub-perfect power (a perfect power minus 1) specifically 4^5 - 1 and 2^10 - 1.^[3] The latter of these makes it a Mersenne number,^[4] 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).^[5]

It is a Stirling number of the second kind, specifically ${\displaystyle \textstyle \left\{{11 \atop 2}\right\}}$.^[6]

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

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.^[8]

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

See also

• AD 1023