1023 (number)
| ||||
|---|---|---|---|---|
| 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 | |||
| Binary | 11111111112 | |||
| Ternary | 11012203 | |||
| Senary | 44236 | |||
| Octal | 17778 | |||
| Duodecimal | 71312 | |||
| Hexadecimal | 3FF16 | |||
1023 (one thousand [and] twenty-three) is the natural number following 1022 and preceding 1024.
In mathematics
1023 is the tenth Mersenne number of the form .[1]
In binary, it is also the tenth repdigit 11111111112 as all Mersenne numbers in decimal are repdigits in binary.
It is equal to the sum of five consecutive prime numbers 193 + 197 + 199 + 211 + 223.[2]
It is the number of three-dimensional polycubes with 7 cells.[3]
1023 is the number of elements in the 9-simplex, as well as the number of uniform polytopes in the tenth-dimensional hypercubic family , and the number of noncompact solutions in the family of paracompact honeycombs that shares symmetries with .
In computing
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.
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 (i.e. 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.[4]
See also
- The year 1023 AD
References
- ^ Sloane, N. J. A. (ed.). "Sequence A000225 (Mersenne numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-01.
- ^ Sloane, N. J. A. (ed.). "Sequence A034964 (Sums of five consecutive primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-01.
- ^ Sloane, N. J. A. (ed.). "Sequence A000162 (Number of 3-dimensional polyominoes (or polycubes) with n cells.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-01.
- ^ Sloane, N. J. A. (ed.). "Sequence A008949 (Triangle read by rows of partial sums of binomial coefficients...also dimensions of Reed-Muller codes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-01.