# Decimal To Binary Calculator + Online Solver With Free Steps

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The** Decimal to Binary Calculator** is a free online tool for converting **decimal numbers to binary numbers**. Decimal numerals are significant because they are a standard system that is widely utilized in everyday life.

**It has a base of ’10’, and the numbers in it range from ‘0’ to ‘9’. **It is among the oldest numerical systems in existence. The binary system, on the other hand, is the basis of computer engineering and information technology.

It is commonly used in networking and computer programming.

## What Is a Decimal To Binary Calculator?

**The Decimal to Binary Calculator is an online calculator that transforms a value from decimal format to binary format. Simple techniques are used to change a base 10 number to a base 2 number.**

As an example, the binary equivalent of the decimal number $12_{10}$ is $1100_2$.

The **binary number system is a numerical system that operates essentially in the same way as the decimal number system**, which is probably more often used. The binary number system uses 2, whereas the decimal number system is based on the number 10.

Moreover, whereas the binary system only employs the digits 0 and 1, each of them being referred to as a bit, the decimal system uses digits 0 through 9 as well.

In addition to these variations, the decimal system’s rules apply to calculations using **addition, subtraction, multiplication, and division**.

## How To Use a Decimal To Binary Calculator?

You can use the **Decimal to Binary Calculator** by following the precise step-by-step instructions provided; the calculator will provide you with the appropriate results. Therefore, you can adhere to the guidelines provided to obtain the **Binary Number value** for the provided data points.

### Step 1

The provided decimal value should be entered in the appropriate input fields.

### Step 2

When you click the “**Submit**” button, a step-by-step explanation of how to convert a given **decimal value to a binary number** will be displayed along with the result.

## How Does a Decimal To Binary Calculator Work?

The **Decimal to Binary Calculator** works byÂ repeatedlyÂ dividing the input decimal number by 2 to convert it from decimal to binary. The remainders are then recorded until the final quotient is equal to 0.

Following this, these residues are written in **reverse order** to produce the provided decimal number’s binary equivalent.

The majority of us utilize the **decimal number system** daily. The decimal system, commonly interpreted as the denary system, is a base-10 numbering system with the following 10 digits i.e., 0 to 9.

Binary numbers, often known as base 2 numbers, are the basis of computer systems because they only have two digits, 0 and 1.

As a result, they may be employed with **modern transistors**, which are used to create modern computer processors, as well as electrical and mechanical switches, with ease.

The given **decimal** can be converted to binary using a variety of techniques, including formulas, the division method, and more. You will learn how to convert decimal values to binary using the division method in this section.

Follow the steps listed below to transform decimal numbers into binary numbers:

### Step 1

Divide the specified decimal value by the number “2,” which displays the outcome and any leftovers.

### Step 2

The outcome will be whole if the specified decimal value is even. The remainder is “0.”

### Step 3

If the specified decimal number is odd, the division of the outcome is improper. The remaining value is “1”.

### Step 4

The appropriate binary number can be achieved by arranging all the remainders so that the **Least Significant Bit (LSB)** is at the head and the **Most Significant Bit (MSB)** is at the bottom.

There are several ways to translate decimal integers into **binary**. The basis of a number changes from 10 to 2 when it is converted from decimal to binary.

It should be noted that every **decimal number** has a binary equivalent. The first 30 whole integers are shown as a decimal to binary chart in the table below.

DecimalNumber | BinaryNumber | HexNumber |

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 |

## Solved Examples

Let’s solve some examples to better understand the **Decimal to Binary Calculator**.

### Example 1

Convert $ 160_{10} $ to binary Number

#### Solution

Decimal Number = $ 160_{10} $

Divide by 2 | Result | Remainder | Binary Value |

160 Ã· 2 | 80 | 0 | 0 (LSB) |

80 Ã· 2 | 40 | 0 | 0 |

40 Ã· 2 | 20 | 0 | 0 |

20 Ã· 2 | 10 | 0 | 0 |

10 Ã· 2 | 5 | 0 | 0 |

5 Ã· 2 | 2 | 1 | 1 |

2 Ã· 2 | 1 | 0 | 0 |

1 Ã· 2 | 0 | 1 | 1 (MSB) |

Therefore, $ 160_{10} = 10100000_2 $

### Example 2

Convert 195.25 into binary.

#### Solution

$ \frac{195}{2}Â = 97 $ with remainder 1

$ \frac{97}{2} = 48 $ with remainder 1

$ \frac{48}{2} = 24 $ with remainder 0

$ \frac{24}{2} = 12 $ with remainder 0

$ \frac{12}{2} = 6 $ with remainder 0

$ \frac{6}{2} = 3 $ with remainder 0

$ \frac{3}{2} = 1 $ with remainder 1

$ \frac{1}{2} = 0 $ with remainder 1

As a result, 195’s binary estimation is 11000011.

The fractional portion of the provided integer must now be converted to binary.

Consider multiplying “0.25” by “2,” and note the integer and fractional components that result. Repeatedly multiplying the final fractional part by “2” results in a final fractional component that is equal to zero.

To create the comparable binary number, we must next write the integer components from each multiplication result.

0.25 Ã— 2 = 0 + 0.5

0.5 Ã— 2 = 1 + 0

Here, ‘0.25’ is equivalent to the binary number ‘0.01’.

**Therefore, $ (195.25)_{10} = (11000011.01)_2 $**