1010100001101

1010100001101 is a binary number. Binary is a base-2 numeral system that uses only two symbols, typically 0 and 1. It is the fundamental language of digital computing. In this system, each digit represents a power of 2, starting from the rightmost digit as 2^0, then 2^1, 2^2, and so on, moving left.

To convert 1010100001101 from binary to decimal, we multiply each digit by its corresponding power of 2 and sum the results. Starting from the right:

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

This calculation results in:

1 + 0 + 4 + 8 + 0 + 0 + 0 + 0 + 256 + 0 + 1024 + 0 + 4096 = 5389.

Therefore, the binary number 1010100001101 is equivalent to the decimal number 5389. Binary representations are crucial in computer science for representing data, instructions, and states within electronic circuits.