What numeral system uses only the digits 1 and 0?

The numeral system that uses only the digits 1 and 0 is the binary numeral system. This system is the foundation of digital computing and electronic systems because it aligns perfectly with the two states of a binary switch: on (1) and off (0). In binary, every digit position represents a power of 2, starting from 2^0 on the right. This simplicity allows for efficient data processing and storage in computers, where operations can be performed using basic logical operations.

In contrast, the decimal numeral system utilizes ten digits (0-9), making it unsuitable for representing data solely with 1s and 0s. The octal numeral system operates with eight digits (0-7), and the hexadecimal numeral system incorporates sixteen digits (0-9 and A-F). These systems, while useful in various applications, do not adhere to the binary principle of using only two distinct symbols. Thus, the binary numeral system is specifically designed for applications that require a clear representation of two states, making it the correct choice for this question.