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How does each position in a binary number relate to powers of two?

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In the binary number system, which serves as the foundation for digital computers, each digit position represents an increasing power of 2, starting from the rightmost position.1

While the decimal system uses powers of 10 for its positions (1, 10, 100, etc.), the binary system assigns values based on the base 2. Moving from right to left, each position corresponds to $2^{n}$ , where $n$ is the position index starting at 0.12

For example:
* The rightmost position represents $2^{0}$ (1).
* The second position from the right represents $2^{1}$ (2).
* The third position represents $2^{2}$ (4).
* The fourth position represents $2^{3}$ (8).

Each bit in a binary number is multiplied by its corresponding power of 2, and the sum of these values determines the total decimal equivalent. This positional structure allows computers to represent complex numerical and logical information using only two states, typically symbolized as 0 and 1.213