How many different combinations can be made using a binary system?

In a binary system, each position can represent either a 0 or a 1. The number of different combinations that can be generated depends on the number of digits in the binary system. Specifically, the formula to calculate the total number of combinations is (2^n), where (n) represents the number of binary digits (or bits).

If we consider an 8-bit binary number, for example, we would calculate (2^8). This results in 256 possible combinations (ranging from 00000000 to 11111111). The number 256 signifies that with 8 bits, you can represent a total of 256 unique values.

Therefore, the correct answer is indeed 256, confirming the role of binary digits in determining the range of possible combinations in binary encoding. The other figures, such as 128, 512, and 1024, correspond to different configurations of binary digits. For instance, 128 represents (2^7) (7 bits), 512 is (2^9) (9 bits), and 1024 is (2^{10}) (10 bits). Each of these values emerges from utilizing a different number of bits, showcasing how combinations exponentially increase