# Binary Numeral System

## Binary Numeral System

Positional numeral system that groups objects by two and only uses the digits 0 and 1.

The binary numeral system is a base 2 system. However, in the binary system, the digit 2 does not exist. The binary numeral system is also a positional numeral system like the one that we can use in the decimal numeral system.

### Notation

In some contexts, to distinguish a number written in binary notation from a number written in decimal notation, we use an index, like this:  $$1101011_2 = 107_{10}$$ or even $$1101011_{deux}=107_{dix}$$.

### Example

The binary number 1101011 can be translated to base 10 like this:
$$(1 × 2^6)+(1 × 2^5)+(0 × 2^4)+(1 × 2^3)+(0 × 2^2)+(1 × 2^1)+(1 × 2^0) = 107$$

### Educational Note

The binary numeral system is the foundation of computer systems: 1 → closed circuit, 0 → open circuit.
It’s also a logical system with two values that are either true (1) or false (0), often used in propositional algebra.