Binary to Decimal Conversion »

## How to convert decimal to binary

#### Conversion steps:

- Divide the number by 2.
- Get the integer quotient for the next iteration.
- Get the remainder for the binary digit.
- Repeat the steps until the quotient is equal to 0.

#### Example #1

Convert 13_{10} to binary:

Division by 2 |
Quotient | Remainder | Bit # |
---|---|---|---|

13/2 | 6 | 1 | 0 |

6/2 | 3 | 0 | 1 |

3/2 | 1 | 1 | 2 |

1/2 | 0 | 1 | 3 |

So 13_{10} = 1101_{2}

#### Example #2

Convert 174_{10} to binary:

Division by 2 |
Quotient | Remainder | Bit # |
---|---|---|---|

174/2 | 87 | 0 | 0 |

87/2 | 43 | 1 | 1 |

43/2 | 21 | 1 | 2 |

21/2 | 10 | 1 | 3 |

10/2 | 5 | 0 | 4 |

5/2 | 2 | 1 | 5 |

2/2 | 1 | 0 | 6 |

1/2 | 0 | 1 | 7 |

So 174_{10} = 10101110_{2}

## Decimal to binary conversion table

Decimal Number |
Binary Number |
Hex Number |
---|---|---|

0 | 0 | 0 |

1 | 1 | 1 |

2 | 10 | 2 |

3 | 11 | 3 |

4 | 100 | 4 |

5 | 101 | 5 |

6 | 110 | 6 |

7 | 111 | 7 |

8 | 1000 | 8 |

9 | 1001 | 9 |

10 | 1010 | A |

11 | 1011 | B |

12 | 1100 | C |

13 | 1101 | D |

14 | 1110 | E |

15 | 1111 | F |

16 | 10000 | 10 |

17 | 10001 | 11 |

18 | 10010 | 12 |

19 | 10011 | 13 |

20 | 10100 | 14 |

21 | 10101 | 15 |

22 | 10110 | 16 |

23 | 10111 | 17 |

24 | 11000 | 18 |

25 | 11001 | 19 |

26 | 11010 | 1A |

27 | 11011 | 1B |

28 | 11100 | 1C |

29 | 11101 | 1D |

30 | 11110 | 1E |

31 | 11111 | 1F |

32 | 100000 | 20 |

64 | 1000000 | 40 |

128 | 10000000 | 80 |

256 | 100000000 | 100 |

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