Binary is a numbering system used to express numbers in 2 states. These two states are 0 and 1. The binary numbering system is very important for computer and IT systems because of the different types of hardware using a binary system like CPU, RAM, GPU, HDD, NIC, etc.

## Binary Values

Binary numbering system provides two values named and `1`

. There is no number like `3`

, `5`

or similar in binary. Computers mainly use these binary values in order to process, read, write data.

## Boolean Logic

Binary numbers are highly related with the boolean logic. Boolean Logic is a logic which is mainly used in computers and mathematics. binary values are used to express the false logic where `1`

is used to express the true logic. We can also use different logic operators like `AND`

, `OR`

, `EXOR`

etc. Here are some Boolean Logic calculations with binary values.

```
1 AND 1 = 1
1 OR 0 = 1
1 AND 0 = 0
1 XOR 0 =1
1 XOR 1 = 0
```

## Binary and Decimal Numbers

Binary numbers can cen be converted into decimal numbers and vise versa. For example `11`

binary value is equal to `3`

in decimal numbering system.

Decimal Value | Binary Value | Base-2 Representation |
---|---|---|

n/a | ||

1 | 1 | 2 |

2 | 10 | 2^{1} |

3 | 11 | 2^{1} + 2 |

4 | 100 | 2^{2} |

5 | 101 | 2^{2}+ 2 |

6 | 110 | 2^{2} + 2^{1} |

7 | 111 | 2^{2} + 2^{1} + 2 |

8 | 1000 | 2^{3} |

9 | 1001 | 2^{3} + 2 |

10 | 1010 | 2^{3} + 2^{1} |

64 | 1000000 | 2^{6} |

256 | 100000000 | 2^{8} |

1024 | 10000000000 | 2^{10} |