The number 1024 in binary is represented as 10000000000. In the binary system, which uses only two digits, 0 and 1, each position represents a power of 2. Therefore, 1024 is calculated as 2 raised to the power of 10, or 2^10. In computing, 1024 is significant because it is often used to define data sizes. For example, 1 kilobyte (KB) is equal to 1024 bytes. This is due to the binary nature of computers, where memory and storage capacities are typically measured in powers of 2, making 1024 a common reference point in computer science.