# Decimal to Binary Converter

Use this online converter a.k.a. decimal to binary calculator to easily convert decimals to binary numbers.

*Quick navigation:*

- Conversion of decimals to binary numbers
- How to convert decimal to binary
- Decimal to binary conversion table

* * Conversion of decimals to binary numbers

Decimals are numbers represented in the decimal positional numeral system (radix / base 10) while binary numbers are numbers represented in the binary positional numeral system which has a base of 2. While the decimals are in ubiquitous use in both our daily life and in science, engineering, etc. binary numbers are not something most people encounter unless they take a course in computer architecture or computer science.

Binary numbers are important in computer systems since information is represented in them as the presence or absence of an electrical impulse (presence is stored as a 1, absence as stored as a 0). Therefore, some binary math and decimal to binary conversions might need to be done as a part of your education. If that is the case, our converter above should be of great use. If you need to perform the conversion by hand, a step-by-step guide is available below.

* * How to convert decimal to binary

Let us say the number we want to convert from decimal to binary is X. Begin the calculation by finding the largest power of 2 ≤ X and denote it by E. Then determine how many times the power of 16 found above goes into X and make not of that. Denote the remainder by Y_{1}.

Repeat the above steps using Y_{n} as a starting value until 2 is larger than the remaining value and assign the remainder to the 2^{0} position, then assign each of the values Y_{1...n} to its respective position and you will have your hex value.

**Example decimal to binary conversion:** Convert 100 in decimal to hex.

1.) Largest power E = 6 (2^{6} = 64 ≤ 100, 2^{7} = 128 ≥ 100)

2.) 100 / 2^{6} = 1 (36 remainder); Y_{1} = 1

3.) Largest power E = 5 (2^{5} = 32 ≤ 36, 2^{6} = 64 ≥ 36)

4.) 32 / 2^{5} = 1 (4 remainder); Y_{2} = 1

5.) Largest power E = 2 (2^{2} = 4 ≤ 4, 2^{3} = 8 ≥ 4)

6.) 4 / 2^{2} = 0 (0 remainder); Y_{3} = 0

7.) 0 < 2; end.

For each power you have used place in its position. For the remainder place zeroes. In this case we've used powers of 2, 5 and 6, therefore the result is: **11**00**1**00 (**1** · 2^{6} + **1** · 2^{5} + 0 · 2^{4} + 0 · 2^{3} + **1** · 2^{2} + 0 · 2^{1} + 0 · 2^{0}).

Since the above process for converting decimals to binary numbers becomes quite tedious for larger numbers, we recommend using our online converter instead.

* * Decimal to binary conversion table

Decimal | Binary |
---|---|

0 | 0 |

1 | 1 |

2 | 10 |

3 | 11 |

5 | 101 |

10 | 1010 |

11 | 1011 |

12 | 1100 |

13 | 1101 |

14 | 1110 |

15 | 1111 |

50 | 110010 |

63 | 111111 |

100 | 1100100 |

1000 | 1111101000 |

10000 | 10011100010000 |

The above table showcases just a couple of key conversions. It cannot really replace a calculator in converting a decimal number to its binary equivalent.

#### Cite this converter & page

If you'd like to cite this online converter resource and information as provided on the page, you can use the following citation:

Georgiev G.Z., *"Decimal to Binary Converter"*, [online] Available at: https://www.gigacalculator.com/converters/convert-decimal-to-binary.php URL [Accessed Date: 29 May, 2023].