# Decimal to Binary

In **decimal to binary** conversion, we convert a decimal number to binary number. In the number system, we 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.

## Decimal to Binary

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 gives the output into decimal form again. Now, we have to 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 find the equivalent binary number from a decimal number.

## Decimal to Binary Table

In order to convert from decimal to binary number system, you should remember the decimal to the binary table to solve the problems in an easy way with an accurate solution. Here 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 where the Least Significant Bit (LSB) at the top and Most Significant Bit (MSB) at the bottom.

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 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}