# INTRODUCTION

Hey guys, In today blog we are going to discuss **“how to convert decimal into binary number system”**

Let get started,

In the previous blog, I told you about **“how to convert binary to decimal numbers”**. So, now we are going to learn how to convert a decimal number into binary numbers system.

Before we start, let take a recap about decimal and binary number:

A **decimal number** is a number that uses the digit **0 to 9 (0,1,2,3,4,5,6,7,8,9)** to represent the number and their base is **“10”**. Some examples of decimal numbers like 65, 29,185, 3354, 75689, etc. On the other hand, A **binary number** is a number that uses only two-digit **“0”** and **“1”** and its base is 2. Some examples of binary number are- 101, 11001, 001001, 11001010101, etc.

If you want to know this topic in more detail then go to this link **“Computer Number System”**.

Now, let discuss how to calculate:

## How to Convert Decimal Into Binary Number System

I will explain this to you with Division method So, that you can understand easily.

### Now, lets do some examples:

**Example 1: **Convert the decimal number **98 _{10}** into Binary form?

**Ans:**

Decimal No. Ã· by 2 | Quotient | Remainder | Places |
---|---|---|---|

98 Ã· 2 | 49 | 0 | First Place=2^{0} |

49 Ã· 2 | 24 | 1 | Second Place=2^{1} |

24 Ã· 2 | 12 | 0 | Third Place=2^{2} |

12 Ã· 2 | 6 | 0 | Fourth Place=2^{3} |

6 Ã· 2 | 3 | 0 | Fifth Place=2^{4} |

3 Ã· 2 | 1 | 1 | Sixth Place=2^{5} |

1 Ã· 2 | 0 | 1 | Seventh Place=2^{6} |

Now, write all the remainder in places wise (Seventh to First Place) = 1100010

= Hence, the binary no. is **(1100010) _{2}**

**Example 2:** Convert the decimal number **164 _{10}** into binary form?

**Ans:**

Decimal no. Ã· by 2 | Quotient | Remainder | Places |
---|---|---|---|

164 Ã· 2 | 82 | 0 | First Place=2^{0} |

82 Ã· 2 | 41 | 0 | Second Place=2^{1} |

41 Ã· 2 | 20 | 1 | Third Place=2^{2} |

20 Ã· 2 | 10 | 0 | Fourth Place=2^{3} |

10 Ã· 2 | 5 | 0 | Fifth Place=2^{4} |

5 Ã· 2 | 2 | 1 | Sixth Place=2^{5} |

2 Ã· 2 | 1 | 0 | Seventh Place=2^{6} |

1 Ã· 2 | 0 | 1 | Eighth Place=2^{7} |

Now, Write all the remainder in places wise (Eighth to First Place) = 10100100

= Hence, the decimal no. is **(10100100) _{2}**

**Example 3: **Convert the decimal number **289 _{10}** into binary form?

**Ans:**

Decimal no. Ã· by 2 | Quotient | Remainder | Places |
---|---|---|---|

289 Ã· 2 | 144 | 1 | First Place=2^{0} |

144 Ã· 2 | 72 | 0 | Second place=2^{1} |

72 Ã· 2 | 36 | 0 | Third Place=2^{2} |

36 Ã· 2 | 18 | 0 | Fourth Place=2^{3} |

18 Ã· 2 | 9 | 0 | Fifth Place=2^{4} |

9 Ã· 2 | 4 | 1 | Sixth Place=2^{5} |

4 Ã· 2 | 2 | 0 | Seventh Place=2^{6} |

2 Ã· 2 | 1 | 0 | Eighth Place=2^{7} |

1 Ã· 2 | 0 | 1 | Ninth Place=2^{8} |

Now, write all the remainder in places wise (Ninth to First place) = 100100001

= Hence, the binary no. is **(100100001) _{2}**

**Example 4: **Convert the decimal number **3468 _{10}** into binary form?

**Ans:**

Decimal no. Ã· by 2 | Quotient | Remainder(Digit) | Places |
---|---|---|---|

3468 Ã· 2 | 1734 | 0 | First Place=2^{0} |

1734 Ã· 2 | 867 | 0 | Second Place=2^{1} |

867 Ã· 2 | 433 | 1 | Third Place=2^{2} |

433 Ã· 2 | 216 | 1 | Fourth Place=2^{3} |

216 Ã· 2 | 108 | 0 | Fifth Place=2^{4} |

108 Ã· 2 | 54 | 0 | Sixth Place=2^{5} |

54 Ã· 2 | 27 | 0 | Seventh Place=2^{6} |

27 Ã· 2 | 13 | 1 | Eighth Place=2^{7} |

13 Ã· 2 | 6 | 1 | Ninth Place=2^{8} |

6 Ã· 2 | 3 | 0 | Tenth Place=2^{9} |

3 Ã· 2 | 1 | 1 | Eleventh Place=2^{10} |

1 Ã· 2 | 0 | 1 | Twelfth Place=2^{11} |

Now, write all the remainder inn places wise (Twelfth to First) = 110110001100

= Hence, the decimal no. is **(110110001100) _{2}**

**Example 5:** Convert the decimal number **58976 _{10}** into binary form?

**Ans:**

Decimal no. Ã· by 2 | Quotient | Remainder(Digit) | Places |
---|---|---|---|

58976 Ã· 2 | 29488 | 0 | First Place=2^{0} |

29488 Ã· 2 | 14744 | 0 | Second place=2^{1} |

14744 Ã· 2 | 7372 | 0 | Third Place=2^{2} |

7372 Ã· 2 | 3686 | 0 | Fourth Place=2^{3} |

3686 Ã· 2 | 1843 | 0 | Fifth Place=2^{4} |

1843 Ã· 2 | 921 | 1 | Sixth Place=2^{5} |

921 Ã· 2 | 460 | 1 | Seventh places=2^{6} |

460 Ã· 2 | 230 | 0 | Eighth Places=2^{7} |

230 Ã· 2 | 115 | 0 | Ninth Place=2^{8} |

115 Ã· 2 | 57 | 1 | Tenth Place=2^{9} |

57 Ã· 2 | 28 | 1 | Eleventh Place=2^{10} |

28 Ã· 2 | 14 | 0 | Twelfth Place=2^{11} |

14 Ã· 2 | 7 | 0 | Thirteenth Place=2^{12} |

7 Ã· 2 | 3 | 1 | Fourteen Place=2^{13} |

3 Ã·2 | 1 | 1 | Fifteen Place=2^{14} |

1 Ã· 2 | 0 | 1 | Sixteen Place=2^{15} |

Now, write all the remainder in places wise in downward to upward like (Sixteen to First place) = 1110011001100000

= Hence, the binary no. is **(1110011001100000) _{2}**

Now, we will do the question with decimal points and see how they solve

**Example 6:** Convert the decimal number **0.25 _{10}** into binary number?

**Ans:** In decimal point question, we have to do the multiply by 2 until the decimal is not finish.

Decimal no. x by 2 | Result |
---|---|

0.25 x 2= 0.5 | 0 |

0.5 x 2= 1.0 | 1 |

Our answer is after point is 01. It means our answer is 0.01

=Hence, our final answer is **0.01 _{2}**

Now let move to the other example

**Example 7:** Convert the decimal number **0.15625 _{10}** into binary form?

**Ans:**

Decimal no. x by 2 | Result |
---|---|

0.15625 x 2= 0.3125 | 0 |

0.3125 x 2= 0.625 | 0 |

0.625 x 2= 1.25 | 1 |

0.25 x 2= 0.5 | 0 |

0.5x 2 = 1 | 1 |

In the decimal point question we will write from upward to downward = 00101

Hence, the binary number is **0.00101**_{2}

**Example 8:** Convert the decimal number **25.625**_{10} into binary form.

**Ans:** In this number 25.625, we have to solve firstly **25 _{10}** into binary in and then after

**0.625**. After that, we will sum the output of

_{10}**25**and

_{10}**0.625**.

_{10}Example = (**output of 25 +output of 0.625**)= Final answer = (…………)_{2}

**Step1:** For now, we have to solve **25 _{10}** into binary

Decimal no. Ã· by 2 | Quotient | Remainder | Places |
---|---|---|---|

25 Ã· 2 | 12 | 1 | First Place=2^{0} |

12 Ã· 2 | 6 | 0 | Second Place=2^{1} |

6 Ã· 2 | 3 | 0 | Third Place=2^{2} |

3 Ã· 2 | 1 | 1 | Fourth Place=2^{3} |

1 Ã· 2 | 0 | 1 | Fifth Place=2^{4} |

Write all the remainder in places wise from fifth to first place = 11001

= Hence, the binary number is **(11001) _{2}**

**Step 2:** Now, we to solve **0.625 _{10}** into binary

As you in the decimal point question we have to do multiply with 2

Decimal no. x by 2 | Resultant integer part (R) |
---|---|

0.625 x 2= 1.25 | 1 |

0.25 x 2= 0.5 | 0 |

0.5 x 2= 1 | 1 |

we have to write all the result from upward to downward manner = 101

=Hence, the binary no. is **0.101 _{2}**

**Final St**e**p:** Output of 25_{10} + Output of 0.625_{10} = (11001_{2} + 0.101_{10} )

Hence, the final answer is** 11001.101 _{2}**

## Conclusion:

I hope you guys liked our today’s blog. If you have any type of query then tell me in the comment section and also give us feedback about our blog in the comment section.

Thank you so much for reading our full blog ðŸ˜Š