Which counting system uses base-2 and consists of only 0s and 1s?

The counting system that uses base-2 and consists solely of the digits 0 and 1 is binary. In this system, each digit represents a power of 2, which is foundational to computer science and digital electronics. Computers operate using binary because they work with two states: on (1) and off (0).

In contrast, the decimal system is based on base-10 and includes the digits 0 through 9. The hexadecimal system operates on base-16, featuring digits 0-9 along with the letters A-F to represent values. Octal, on the other hand, utilizes base-8 and includes the digits 0 through 7. Each of these counting systems serves specific purposes, but only binary is characterized by its exclusive use of 0s and 1s, making it the correct choice for this question.