10101100010

10101100010 is a binary number. In base 2, the digits can only be 0 or 1. This specific sequence represents a value in the decimal system. To convert this binary number to decimal, we multiply each digit by the corresponding power of 2, starting from the rightmost digit. The rightmost digit is 0, multiplied by 2^0 (which is 1). The next digit to the left is 1, multiplied by 2^1 (which is 2). Continuing this process from right to left: (0 * 2^0) + (1 * 2^1) + (0 * 2^2) + (0 * 2^3) + (0 * 2^4) + (1 * 2^5) + (1 * 2^6) + (0 * 2^7) + (1 * 2^8) + (0 * 2^9) + (1 * 2^10). This calculation yields a decimal value. Performing the arithmetic, we have (0 * 1) + (1 * 2) + (0 * 4) + (0 * 8) + (0 * 16) + (1 * 32) + (1 * 64) + (0 * 128) + (1 * 256) + (0 * 512) + (1 * 1024). Summing these products, we get 0 + 2 + 0 + 0 + 0 + 32 + 64 + 0 + 256 + 0 + 1024, which equals 1378. Therefore, the binary number 10101100010 is equivalent to the decimal number 1378. Binary numbers are fundamental in computer science and digital electronics, serving as the basic language for all data processing.