1000100010010010

The sequence 1000100010010010 is a binary number. In base-2, it is represented as a string of ones and zeros. To understand its value in the more familiar decimal (base-10) system, each digit's position corresponds to a power of 2, starting from the rightmost digit as 2^0, the next as 2^1, and so on.

Reading from right to left, the digits are at positions 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15. The decimal value is calculated by summing the products of each digit and its corresponding power of 2. For 1000100010010010, the ones are at positions 1, 4, 8, and 15. Therefore, the decimal equivalent is (1 * 2^15) + (0 * 2^14) + ... + (1 * 2^4) + (0 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0). This results in 32768 + 0 + 0 + 0 + 256 + 0 + 0 + 0 + 16 + 0 + 0 + 0 + 2 + 0 = 33042.

As a 16-bit binary number, it can represent a range of values from 0 (0000000000000000) to 65535 (1111111111111111). The specific sequence 1000100010010010 falls within this range. Binary representations are fundamental in computer science and digital electronics, where data is processed and stored using these two states.

---