# Base

## Mathematics

The basis for a numbering system, the base indicates how many unique digits are used in representing all numbers.

For example, in base 3, digits are often represented as: 0, 1, 2.

The number 143 in the decimal system is equivalent to 12022 in base 3:

Decimal: $143 = 1 \times 10^2 + 4 \times 10^1 + 3 \times 10^0$

Base 3: $12022 = 1 \times 3^4 + 2 \times 10^3 + 0 \times 10^2 + 2 \times 10^1 + 2\times 10^0$

### Common bases in computing

Computers naturally work in base 2 (binary). A single binary digit is called a bit.

A group of 3 binary digits can be repesented by a single octal digit.

A group of 4 binary digits is sometimes called a nybble (or nibble). A nybble can be represented by one hexadecimal digit.

A group of 8 binary digits is a byte. A single byte can be represented by 2 hexadecimal digits.

For example, 10110111 in binary is equivalent to B7 in hexadecimal.

## Chemistry

bases are the opposite of acids. bases combine with acids to form salts.