10000001010011

10000001010011 is a binary number. In the decimal system, this number translates to 16427. Binary numbers are a base-2 numeral system, meaning they only use two digits: 0 and 1. Each digit in a binary number represents a power of 2, starting from the rightmost digit as 2^0, then 2^1, 2^2, and so on. To convert 10000001010011 to decimal, we sum the products of each digit and its corresponding power of 2.

In this case, the calculation is as follows:

1 * 2^13 + 0 * 2^12 + 0 * 2^11 + 0 * 2^10 + 0 * 2^9 + 0 * 2^8 + 0 * 2^7 + 1 * 2^6 + 0 * 2^5 + 1 * 2^4 + 0 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0

= 8192 + 0 + 0 + 0 + 0 + 0 + 0 + 64 + 0 + 16 + 0 + 0 + 2 + 1

= 8192 + 64 + 16 + 2 + 1

= 8275

Therefore, the binary number 10000001010011 is equivalent to the decimal number 8275. Binary representations are fundamental in computer science and digital electronics, as they are the basis for how computers store and process information.