In which system is 2^n utilized for value representation?

The binary system utilizes ( 2^n ) for value representation because it is based on two symbols: 0 and 1. In this system, each digit (or bit) represents a power of 2, depending on its position. For example, in an 8-bit binary number, the leftmost bit represents ( 2^7 ), the next ( 2^6 ), and so on, down to the rightmost bit, which represents ( 2^0 ). This system is foundational in digital electronics and computer science, as it aligns perfectly with the on/off states of electronic circuits (where 0 can represent off and 1 can represent on).

By contrast, the decimal system utilizes ( 10^n ) for value representation, the hexadecimal system uses ( 16^n ), and the quaternary system is based on ( 4^n ). Each of these systems has its own base and corresponding values but does not rely on powers of 2 like the binary system does. This fundamental property of binary is what makes it uniquely suited for tasks in computing, where simplicity in representation leads to efficiency in processing.