10100010011000

10100010011000 is a binary number. In the decimal system, this number translates to 10680. Binary is a base-2 numeral system, meaning it uses only two symbols, typically 0 and 1. These digits are known as bits. The position of each bit in a binary number determines its value, with each position representing a power of 2. Starting from the rightmost bit, the positions represent 2^0, 2^1, 2^2, and so on, increasing to the left.

To convert 10100010011000 from binary to decimal, we multiply each bit by its corresponding power of 2 and sum the results. The binary number 10100010011000 can be expanded as follows:

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

This calculation results in:

8192 + 0 + 2048 + 0 + 0 + 0 + 128 + 0 + 0 + 16 + 8 + 0 + 0 + 0 = 10392.

Therefore, the binary number 10100010011000 is equivalent to the decimal number 10392. Binary representation is fundamental in computing and digital electronics, as it forms the basis of how data is stored and processed.