101101001000

101101001000 is a binary number. In binary, each digit represents a power of two. The rightmost digit represents 2^0 (or 1), the next digit to the left represents 2^1 (or 2), and so on. To convert 101101001000 to its decimal (base-10) equivalent, we sum the powers of two corresponding to the positions of the '1's.

Starting from the rightmost digit, the positions are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. The binary number 101101001000 has '1's at positions 3, 7, 8, 10, and 11. Therefore, its decimal value is calculated as follows: (1 2^11) + (0 2^10) + (1 2^9) + (1 2^8) + (0 2^7) + (1 2^6) + (0 2^5) + (0 2^4) + (1 2^3) + (0 2^2) + (0 2^1) + (0 2^0).

This sum simplifies to: 2048 + 0 + 512 + 256 + 0 + 64 + 0 + 0 + 8 + 0 + 0 + 0 = 2888. Thus, the binary number 101101001000 is equivalent to the decimal number 2888. Binary representations are fundamental in computer science and digital electronics, where they are used to represent data and instructions. Each sequence of binary digits can be interpreted in various ways depending on the context, such as representing integers, characters, or machine code.