100100000010010

The sequence 100100000010010 is a binary number. Binary is a base-2 numeral system that uses only two symbols, typically "0" and "1", to represent numbers. In the binary system, each digit's position represents a power of 2, starting from 2^0 on the rightmost side.

To convert 100100000010010 from binary to decimal, we can multiply each digit by its corresponding power of 2 and sum the results. Starting from the rightmost digit as 2^0, the number 100100000010010 represents:

1 * 2^14 + 0 * 2^13 + 0 * 2^12 + 1 * 2^11 + 0 * 2^10 + 0 * 2^9 + 0 * 2^8 + 0 * 2^7 + 0 * 2^6 + 0 * 2^5 + 0 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0

This calculation results in:

16384 + 0 + 0 + 2048 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 8 + 0 + 2 + 0 = 18442

Therefore, the binary number 100100000010010 is equivalent to the decimal number 18442. Binary representations are fundamental in computer science and digital electronics, as they form the basis of how computers store and process information.