1023 (number)

1023 (one thousand [and] twenty-three) is the natural number following 1022 and preceding 1024.

Mathematics
1023 is the tenth non-trivial Mersenne number of the form $$2^{n}-1$$. In binary, it is also the tenth repdigit 11111111112 as all Mersenne numbers in decimal are repdigits in binary.

As a Mersenne number, it is the first non-unitary member of the eleventh row (left to right) in the triangle of Stirling partition numbers

$$(1, \mathbf {1023}, 28501, 145750, 246730, 179487, 63987, 11880, 1155, \mathbf {55}, 1)$$

that appears opposite a triangular number (successively in each row), in its case 55.

It is equal to the sum of five consecutive prime numbers: 193 + 197 + 199 + 211 + 223.

It is equal to the sum of the squares of the first seven consecutive odd prime numbers: 32 + 52 + 72 + 112 + 132 + 172 + 192.

It is the number of three-dimensional polycubes with seven cells.

1023 is the number of elements in the 9-simplex, as well as the number of uniform polytopes in the tenth-dimensional hypercubic family $$\mathrm B_{10}$$, and the number of noncompact solutions in the family of paracompact honeycombs $\tilde T_{9}$ that shares symmetries with $$\mathrm E_{10}$$.

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.