To convert Decimal to Binary, input decimal value in the box below, and then click on the big blue button that says “CONVERT TO BINARY” and your binary is generated, copy it or you can download output file.

Copied to Clipboard.

In decimal number system there only ten (10) digits from 0 to 9. Every number (value) in this decimal system represents with 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The base of this number system is 10, because it has only 10 digits.

**Example: 8062 in decimal (base 10)**

8062_{10} = (8 x 10^{3}) + (0 x
10^{2}) + (6 x 10^{1}) + (2 x
10^{0})

In Binary number system there are only two digits that are 0 and 1. In this number system every number (value) represents with 0 and. The base of binary number system is 2, because it has only two digits.

**Example: What is (110) _{2} in base 10?**

110_{2} = (1 x 2^{2}) + (1 x
2^{1}) + (0 x 1^{0}) = 6_{10}

To convert a number in decimal to a number in binary we have to divide the decimal number by 2 repeatedly, until the quotient of zero is obtained. This method of repeated division by 2 is called the ‘double-dabble’ method. The remainders are noted down for each of the division steps. Then the column of the remainder is read in reverse order i.e., from bottom to top order. We try to show the method with an example shown in Examples.

**Example 1: Convert (26) _{10} into a binary number**

Division | Quotient | Remainder |

26/2 | 13 | 0 |

13/2 | 6 | 1 |

6/2 | 3 | 0 |

3/2 | 1 | 1 |

1/2 | 0 | 1 |

Hence the converted binary number is (11010)_{2}

**Example 2: Convert (139) _{2} into binary number:**

Division | Quotient | Remainder |

139/2 | 69 | 1 |

69/2 | 34 | 1 |

34/2 | 17 | 0 |

17/2 | 8 | 1 |

8/2 | 4 | 0 |

4/2 | 2 | 0 |

2/2 | 1 | 0 |

Hence the converted binary number is (0001011)_{2}

Decimal |
Binary |

0 | 0000 |

1 | 0001 |

2 | 0010 |

3 | 0011 |

4 | 0100 |

5 | 0101 |

6 | 0110 |

7 | 0111 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

11 | 1011 |

12 | 1100 |

13 | 1101 |

14 | 1110 |

15 | 1111 |