How do computers count?

Computers count using the binary system, which involves two distinct states represented by the digits 0 and 1. This system is fundamental to how computers process and store data, as it aligns well with the physical state of electronic components found in computers, such as transistors, which can be either off (0) or on (1).

In binary, each digit represents a power of 2. For example, in the binary number 1011, the calculation is as follows: (1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0), which equals 11 in the decimal system. This characteristic of binary allows computers to efficiently perform arithmetic operations, facilitate data storage, and manage logical operations.

The other number systems mentioned, while relevant in different contexts (like decimal for human counting, hexadecimal for more compact number representation, and octal for certain computing functions), are not used natively by computers for counting or performing core computational tasks. Instead, they often serve as representations or conversions of the underlying binary data.