## About

The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1.

Owing to its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by all modern computers.

## Articles Related

## Counting in binary

It is possible to do arithmetic in base two, e.g. 3+5 is written:

<math> \begin{array}{cccc} & 0 & 0 & 1 & 1 \\ + & 0 & 1 & 0 & 1 \\ \hline & 1 & 0 & 0 & 0 \\ \end{array} </math>

The addition works like normal (base-10) arithmetic, where:

<math> \begin{array}{cccc} & & 1 \\ + & & 1 \\ \hline & 1 & 0 \\ \end{array} </math> where 1 + 1 = 0 with a carry of 1 and 1 + 0 = 1

Subtraction, multiplication, etc. work this way:

<math> \begin{array}{cccc} & & \textit{1} & \textit{1} & & \textit{carried digits} \\ \\ & 0 & 0 & 1 & 1 & \\ + & 0 & 1 & 0 & 1 &\\ \hline & 1 & 0 & 0 & 0 & \\ \end{array} </math>

## Translation in

### Decimal

#### Integer

Using Arabic numerals, binary numbers are commonly written using the symbols 0 and 1.

Number | Binary coding |
---|---|

0 | 0000 |

1 | 0001 |

2 | 0010 |

3 | 0011 |

4 | 0100 |

5 | 0101 |

6 | 0110 |

7 | 0111 |

8 | 1000 |

……. | |

14 | 1110 |

15 | 1111 |

……. |

#### Floating point

1.01 in base-2 notation is 1 + 0/2 + 1/4, or 1.25 in decimal notation.

### Hexadecimal

Binary | Hexadecimal |
---|---|

0 | 0 |

1 | 1 |

10 | 2 |

11 | 3 |

100 | 4 |

101 | 5 |

110 | 6 |

111 | 7 |

1000 | 8 |

1001 | 9 |

1010 | A |

1011 | B |

1100 | C |

1101 | D |

1110 | E |

1111 | F |

Hexadecimal is then to easier write. For example, the binary number “100110110100” is “9B4” in hexadecimal.