# Decimal To Binary Converter

__Mixed Decimal to Binary Converter__

To find the Binary equivalent of given Decimal number using Mixed Decimal Binary Converter, type the Decimal number to be converted in the below given text box. Then press the “Click here to Convert” button for getting the Binary equivalent of the given Decimal number. It is possible to covert any length of Decimal digits. The Decimal to Binary Converter can support both Integer number as well as Real number. It is possible to covert any length of mixed Decimal (Integer with Real) Number to Binary equivalent.

(Enter your Decimal Number in the Below given Text Box)

## Decimal Number System :

The Decimal Number System consist of ten digits such as 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It is an Arabic numbers and which are used for our common use. Because of the Decimal Number System consist of only ten digits and so that the base of the Decimal Number System is 10. The weights of each digit positions in the mixed Decimal Number System are . . . . 10^{3} 10^{2} 10^{1} 10^{0} . 10^{-1} 10^{-2} 10^{-3} 10^{-4} . . . .

## Binary Number System :

The Binary Number System consist of two digits such as 0 and 1. The binary digit 0 means no information and 1 means information. Generally the digital computers are designed on the basis of Binary. However, the electronic circuits are operated with binary signals. Thus all the electronic devices are functioned on the basis of binary. Technically, the binary digit 1(High) indicate that there is an information and 0(Low) indicate that there is no information. Because of the Binary Number System consist of only two digits and so that the base of Binary Number System is 2. The weights of each digit positions in the mixed Binary Number System are . . . . 2^{3} 2^{2} 2^{1} 2^{0} . 2^{-1} 2^{-2} 2^{-3} 2^{-4} . . . .

## How to Convert Decimal to Binary ?

**Convert Integer part of Decimal to Binary**

The Integer part Binary number can be converted into Decimal by two Methods. They are

**Method 1: Short Division by Two with Remainder
Method 2: Descending Powers of Two and Subtraction**

## Decimal to Binary Conversion by using Short Division by Two with Remainder

To Convert the **Integer part** of a given Decimal number to Binary equivalent, we should divide the given decimal number by 2 and write down the remainder on right side of each division. Continue the process (divide the number again and again and write down the remainder on right side of each division) till the given number can be divided by 2. Then write down the remainders from bottom to top to form the Binary equivalent. For Example: Let us find the binary equivalent of decimal (50)_{10}

50 / 2 = 25 ———————– 0

25 / 2 = 12 ———————- 1

12 / 2 = 6 ———————– 0

6 / 2 = 3 ———————— 0

3 / 2 = 1 ———————— 1

———————————– 1

Therefore the binary equivalent of decimal (50)_{10} is (110010)_{2}

## Decimal to Binary Conversion by using Descending Powers of Two and Subtraction

In this method, we should prepare a chart with the powers of two from right hand side to left hand side (The chart should start with 2^{0}).

Step 1: Start with the biggest decimal number of the power of two that will fit in the decimal number to be converted. Subtract the biggest decimal number from the decimal number to be converted.

Step 2: Continue with the next lower power of two that will fit in the remainder decimal number (after the subtraction of step 1).

Step 3: Continue same process again and again until the the next lower power of two that will fit in the remainder decimal number.

Step 3: Then write out the 1’s and 0’s as per the above process. For example:

Let us find the binary equivalent of decimal (50)_{10}

The chart with the powers of two from right hand side to left hand side is

32 16 8 4 2 1

2^{5} 2^{4} 2^{3} 2^{2} 2^{1} 2^{0}

To find the binary equivalent of decimal (50)_{10}

The decimal number of the powers of two needed are 50, 16, 2

50-32=18

18-16=2

2-2=0

Therefore, the binary equivalent of decimal (50)_{10} is (110010)_{2}

**How to Convert Fractional part of Decimal to Binary** ?

To Convert the **Fractional (Real) part** of a given Decimal number to Binary equivalent, we should multiply the given fractional (real) part of the given decimal number by 2 and write down the carries on right side of each multiplication. Continue the process for a minimum of five or six steps. Then write down the carries from Top to bottom to form the Binary equivalent. Moreover, the below example is also done by using Decimal to Binary Conversion method.

## Examples using Decimal to Binary Converter

**Decimal to Binary Conversion Example 1:**

Let us find the binary number of (746.207)_{10} using Decimal to Binary Converter

Given Decimal number : (746.207)_{10}

Binary equivalent of the Decimal number is :

**Integer Part Conversion**:-

__Remainders__

746 / 2 = 373 ——————– 0

373 / 2 = 186 ——————– 1

186 / 2 = 93 ————-=——- 0

93 / 2 = 46 ————–=——- 1

46/ 2 = 23 ————–=——— 0

23 / 2 = 11 ———————- 1

11 / 2 = 5 ———————– 1

5 / 2 = 2 ———————— 1

2 / 2 = 1 ———————— 0

———————————– 1

**Real Part Conversion**:-

__Carries__

0.207 * 2 => 0.414 ——— 0

0.414 * 2 => 0.828 ——— 0

0.828 * 2 => 1.656 ——— 1

0.656 * 2 => 1.312 ——— 1

0.312 * 2 => 0.624 ——— 0

0.624 * 2 => 1.248 ——— 1

Binary equivalent of (746.207)_{10} is (1011101010.001101)_{2}

**Decimal to Binary Conversion Example 2:**

Let us find the binary number of (847638.29184)_{10} using Decimal to Binary Converter

Given Decimal number : (847638.29184)_{10}

Binary equivalent of the Decimal number is :

**Integer Part Conversion**:-

__Remainders__

847638 / 2 = 423819 ————– 0

423819 / 2 = 211909 ————– 1

211909 / 2 = 105954 ————– 1

105954 / 2 = 52977 ————— 0

52977 / 2 = 26488 —————- 1

26488 / 2 = 13244 —————- 0

13244 / 2 = 6622 —————– 0

6622 / 2 = 3311 —————— 0

3311 / 2 = 1655 —————— 1

1655 / 2 = 827 ——————- 1

827 / 2 = 413 ——————– 1

413 / 2 = 206 ——————– 1

206 / 2 = 103 ——————– 0

103 / 2 = 51 ——————— 1

51 / 2 = 25 ———————– 1

25 / 2 = 12 ———————- 1

12 / 2 = 6 ———————– 0

6 / 2 = 3 ———————— 0

3 / 2 = 1 ———————— 1

———————————– 1

**Real Part Conversion**:-

__Carries__

0.29184 * 2 => 0.58368 ——— 0

0.58368 * 2 => 1.16736 ——— 1

0.16736 * 2 => 0.33472 ——— 0

0.33472 * 2 => 0.66944 ——— 0

0.66944 * 2 => 1.33888 ——— 1

0.33888 * 2 => 0.67776 ——— 0

0.67776 * 2 => 1.35552 ——— 1

Binary equivalent of (847638.29184)_{10} is (11001110111100010110.0100101)_{2}

**Decimal to Binary Conversion Example 3:**

Let us find the binary number of (845763.21291)_{10} using Decimal Binary Converter

Given Decimal number : (845763.21291)_{10}

Binary equivalent of the Decimal number is :

**Integer Part Conversion**:-

__Remainders__

845763 / 2 = 422881 ————– 1

422881 / 2 = 211440 ————– 1

211440 / 2 = 105720 ————– 0

105720 / 2 = 52860 ————— 0

52860 / 2 = 26430 —————- 0

26430 / 2 = 13215 —————- 0

13215 / 2 = 6607 —————– 1

6607 / 2 = 3303 —————— 1

3303 / 2 = 1651 —————— 1

1651 / 2 = 825 ——————- 1

825 / 2 = 412 ——————– 1

412 / 2 = 206 ——————– 0

206 / 2 = 103 ——————– 0

103 / 2 = 51 ——————— 1

51 / 2 = 25 ———————– 1

25 / 2 = 12 ———————- 1

12 / 2 = 6 ———————– 0

6 / 2 = 3 ———————— 0

3 / 2 = 1 ———————— 1

———————————– 1

**Real Part Conversion**:-

__Carries__

0.21291 * 2 => 0.42582 ——— 0

0.42582 * 2 => 0.85164 ——— 0

0.85164 * 2 => 1.70328 ——— 1

0.70328 * 2 => 1.40656 ——— 1

0.40656 * 2 => 0.81312 ——— 0

0.81312 * 2 => 1.62624 ——— 1

0.67776 * 2 => 1.35552 ——— 1

Binary equivalent of (845763.21291)_{10} is (11001110011111000011.0011011)_{2}

### Decimal to Binary Converter Chart :

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

0 | 0 |

1 | 1 |

2 | 10 |

3 | 11 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

11 | 1011 |

12 | 1100 |

13 | 1101 |

14 | 1110 |

15 | 1111 |

16 | 10000 |

17 | 10001 |

18 | 10010 |

19 | 10011 |

20 | 10100 |

21 | 10101 |

22 | 10110 |

23 | 10111 |

24 | 11000 |

25 | 11001 |

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