11000100111110

11000100111110 is a binary number. In the decimal system, this number translates to 13014. Binary, also known as base-2, is a numeral system that uses only two symbols, typically 0 and 1. It is the fundamental language of computing, as all digital data is represented using combinations of these two digits. The position of each digit in a binary number signifies a power of two, starting from the rightmost digit as 2^0, then 2^1, 2^2, and so on, moving leftwards.

To convert 11000100111110 from binary to decimal, we multiply each binary digit by its corresponding power of two and sum the results. Starting from the rightmost digit: 0 * 2^0 + 1 * 2^1 + 1 * 2^2 + 1 * 2^3 + 1 * 2^4 + 0 * 2^5 + 0 * 2^6 + 1 * 2^7 + 0 * 2^8 + 0 * 2^9 + 0 * 2^10 + 1 * 2^11 + 1 * 2^12. This calculation yields 0 + 2 + 4 + 8 + 16 + 0 + 0 + 128 + 0 + 0 + 0 + 2048 + 4096 = 6302. Re-calculating with the correct sequence: 0*2^0 + 1*2^1 + 1*2^2 + 1*2^3 + 1*2^4 + 0*2^5 + 0*2^6 + 1*2^7 + 0*2^8 + 0*2^9 + 0*2^10 + 1*2^11 + 1*2^12. This is incorrect. The correct calculation for 11000100111110 is 0*2^0 + 1*2^1 + 1*2^2 + 1*2^3 + 1*2^4 + 0*2^5 + 0*2^6 + 1*2^7 + 0*2^8 + 0*2^9 + 0*2^10 + 1*2^11 + 1*2^12 = 0 + 2 + 4 + 8 + 16 + 0 + 0 + 128 + 0 + 0 + 0 + 2048 + 4096 = 6302. There was an error in the initial decimal conversion. The correct decimal equivalent for 11000100111110 is 6302. This number has 13 digits, meaning it can represent values up to 2^13 - 1, which is 8191.