In **decimal to binary** conversion, we convert a base 10 number to base 2 number by using simple methods. For example, if 12_{10} is a decimal number then its equivalent binary number is 1100_{2}.

Students can learn online here to convert any given decimal number into its equivalent binary number system. In the number system, you may have learned about different types of numbers such as;

- Binary Numbers – Base 2
- Octal Numbers – Base 8
- Decimal Numbers – Base 10
- Hexadecimal Numbers – Base 16

These numbers can be converted from one system to other systems like decimal to binary, decimal to hex, decimal to octal and vice versa. In this article, you are going to learn the conversion of decimal to binary number system along with the conversion steps and examples.

**Also, read:** Decimal To Binary Converter

## Decimal to Binary Conversion

A decimal number has base 10 and a binary number has base 2. In decimal to binary conversion, the base of the number also changes, i.e. from base 10 to base 2. All the decimal numbers have its equivalent binary numbers. These binary numbers are majorly used in computer applications, where it is used for programming or coding purpose. This is because computers understand the language of binary digits, o and 1.

Hence, once we give the input to the computer system in the decimal form, it converts them into binary digits, performs the required operations and provides the output with into decimal form again. Now, learn here how the decimal number can be represented here in binary form. But before learning the steps for conversion, first, let us see the table to know the equivalent binary number for a decimal number.

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## Decimal to Binary Table

To convert numbers from decimal to binary number system, you should remember the decimal to the binary table to solve the problems efficiently with an accurate solution. The decimal to binary conversion up to 20 numbers is given below for reference.

Decimal Number |
Binary Number |

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 |

## How to Convert Decimal Numbers to Binary Numbers?

To convert decimal to binary numbers, proceed the steps given below:

- Divide the given decimal number by “2” where it gives the result along with the remainder.
- If the given decimal number is even, then the result will be whole and it gives the remainder “0”
- If the given decimal number is odd, then the result is not divided properly and it gives the remainder “1”.
- By placing all the remainders in order in such a way, the Least Significant Bit (LSB) at the top and Most Significant Bit (MSB) at the bottom, the required binary number will obtain.

Now, let us convert the given decimal number 294 into a binary number.

Divide by 2 |
Result |
Remainder |
Binary Value |

294 ÷ 2 | 147 | 0 | 0 (LSB) |

147 ÷ 2 | 73 | 1 | 1 |

73 ÷ 2 | 36 | 1 | 1 |

36 ÷ 2 | 18 | 0 | 0 |

18 ÷ 2 | 9 | 0 | 0 |

9 ÷ 2 | 4 | 1 | 1 |

4 ÷ 2 | 2 | 0 | 0 |

2 ÷ 2 | 1 | 0 | 0 |

1 ÷ 2 | 0 | 1 | 1 (MSB) |

Therefore, the binary equivalent for the given decimal number 294_{10} is 100100110_{2}

**294 _{10} =100100110_{2}**

## Decimal to Binary Conversion Solved Examples

**Example 1:** **Convert 160 _{10} to binary Number**

**Solution:**

Given: Decimal Number = 160_{10}

Divide by 2 |
Result |
Remainder |
Binary Value |

160 ÷ 2 | 80 | 0 | 0 (LSB) |

80 ÷ 2 | 40 | 0 | 0 |

40 ÷ 2 | 20 | 0 | 0 |

20 ÷ 2 | 10 | 0 | 0 |

10 ÷ 2 | 5 | 0 | 0 |

5 ÷ 2 | 2 | 1 | 1 |

2 ÷ 2 | 1 | 0 | 0 |

1 ÷ 2 | 0 | 1 | 1 (MSB) |

Therefore, 160_{10} = 10100000_{2}

**Example 2: Convert 17 _{10 }into a binary number**

Solution:

Given: Decimal Number = 17_{10}

Divide by 2 |
Result |
Remainder |
Binary Value |

17 ÷ 2 | 8 | 1 | 1 (LSB) |

8 ÷ 2 | 4 | 0 | 0 |

4 ÷ 2 | 2 | 0 | 0 |

2 ÷ 2 | 1 | 0 | 0 |

1 ÷ 2 | 0 | 1 | 1 (MSB) |

Therefore, 17_{10} = 10001_{2}

### Decimal to Binary Problems

Here are a few questions that are given for students, so that they can solve them and get good practice. Solving these problems will help students to increase their speed and attain good marks in the exams.

- Convert 244
_{10}to its equivalent binary number. - Convert 76
_{10}to binary number. - What is the binary equivalent of decimal number 891
_{10}? - Convert 57
_{10}into a binary number.

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