In computer science and mathematics, the binary number system is a radix 2 number system with 1 and 0 as the two independent digits. The word binary comes from "Bi-" means two. A Binary system is made up of only 1s and 0s. A single binary digit is called a bit like 1001 is four bits long. The binary numbers system is also called as base-2 numeral system.

Binary number system, represents numeric values using binary numbers: typically 0 and 1.

For example: (10010)$_2$ is a binary number.

Decimal numbers can be represented in binary numbers. The first 11 numbers in the binary number system are shown below:

**Decimal to Binary** |

0 |
0 |

1 |
1 |

2 |
10 |

3 |
11 |

4 |
100 |

5 |
101 |

6 |
110 |

7 |
101 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

**Addition and subtraction of binary numbers: **Addition and subtraction of binary numbers is accomplished in the same manner as decimal addition and subtraction. The basic rules for Addition and subtraction of binary numbers are:

**Rules for Addition**

- 0 + 0 = 0
- 1 + 0 = 1
- 0 + 1 = 1
- 1 + 1 = 0 (plus a carry of 1)

**Rules for Subtraction**

- 0 - 0 = 0
- 1 - 1 = 0
- 1 - 0 = 1
- 0 - 1 = 1 (borrow from the next column)