10101110100100

10101110100100 is a binary number. In the decimal system, this number translates to 11620. Binary is a base-2 numeral system, meaning it only uses two digits, 0 and 1, to represent numerical values. Each digit in a binary number represents a power of two, starting from 2^0 on the rightmost side and increasing by one for each position to the left.

To convert 10101110100100 from binary to decimal, we can multiply each digit by its corresponding power of two and sum the results. The rightmost digit corresponds to 2^0, the next to 2^1, and so on. For 10101110100100, this calculation would be:

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

= 8192 + 0 + 2048 + 0 + 512 + 256 + 128 + 0 + 32 + 0 + 0 + 4 + 0 + 0

= 11172.

Binary numbers are fundamental in computer science and digital electronics, as they are the language that computers use to process information.