What method of representing numbers uses base 2 and only the digits 0 and 1?

The method of representing numbers that uses base 2 and only the digits 0 and 1 is known as binary numbers. In the binary system, each digit is referred to as a bit, and it is the fundamental means of data representation in computer systems. Since computers operate using electrical signals, they need a way to represent information in a form that can be easily manipulated and processed. The binary system is ideal for this purpose because the two states (on and off) can be conveniently represented by 1s and 0s.

Understanding binary numbers is essential in fields such as computer science, programming, and digital electronics, where systems rely on binary operations for calculations and decision-making processes. This system contrasts with other numbering systems like the decimal system, which uses base 10 and includes digits from 0 to 9. Other options provided, such as browser, byte, and broadband, refer to different concepts related to computing and data transmission, but do not pertain to the representation of numbers in base 2. Thus, binary numbers are the correct answer, as they are specifically designed to represent values using only two digits.