# 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. ÷ by 2 | Quotient | Remainder | Places |
---|---|---|---|

98 ÷ 2 | 49 | 0 | First Place=2^{0} |

49 ÷ 2 | 24 | 1 | Second Place=2^{1} |

24 ÷ 2 | 12 | 0 | Third Place=2^{2} |

12 ÷ 2 | 6 | 0 | Fourth Place=2^{3} |

6 ÷ 2 | 3 | 0 | Fifth Place=2^{4} |

3 ÷ 2 | 1 | 1 | Sixth Place=2^{5} |

1 ÷ 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. ÷ by 2 | Quotient | Remainder | Places |
---|---|---|---|

164 ÷ 2 | 82 | 0 | First Place=2^{0} |

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

41 ÷ 2 | 20 | 1 | Third Place=2^{2} |

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

10 ÷ 2 | 5 | 0 | Fifth Place=2^{4} |

5 ÷ 2 | 2 | 1 | Sixth Place=2^{5} |

2 ÷ 2 | 1 | 0 | Seventh Place=2^{6} |

1 ÷ 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. ÷ by 2 | Quotient | Remainder | Places |
---|---|---|---|

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

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

72 ÷ 2 | 36 | 0 | Third Place=2^{2} |

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

18 ÷ 2 | 9 | 0 | Fifth Place=2^{4} |

9 ÷ 2 | 4 | 1 | Sixth Place=2^{5} |

4 ÷ 2 | 2 | 0 | Seventh Place=2^{6} |

2 ÷ 2 | 1 | 0 | Eighth Place=2^{7} |

1 ÷ 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. ÷ by 2 | Quotient | Remainder(Digit) | Places |
---|---|---|---|

3468 ÷ 2 | 1734 | 0 | First Place=2^{0} |

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

867 ÷ 2 | 433 | 1 | Third Place=2^{2} |

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

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

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

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

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

13 ÷ 2 | 6 | 1 | Ninth Place=2^{8} |

6 ÷ 2 | 3 | 0 | Tenth Place=2^{9} |

3 ÷ 2 | 1 | 1 | Eleventh Place=2^{10} |

1 ÷ 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. ÷ by 2 | Quotient | Remainder(Digit) | Places |
---|---|---|---|

58976 ÷ 2 | 29488 | 0 | First Place=2^{0} |

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

14744 ÷ 2 | 7372 | 0 | Third Place=2^{2} |

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

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

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

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

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

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

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

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

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

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

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

3 ÷2 | 1 | 1 | Fifteen Place=2^{14} |

1 ÷ 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. ÷ by 2 | Quotient | Remainder | Places |
---|---|---|---|

25 ÷ 2 | 12 | 1 | First Place=2^{0} |

12 ÷ 2 | 6 | 0 | Second Place=2^{1} |

6 ÷ 2 | 3 | 0 | Third Place=2^{2} |

3 ÷ 2 | 1 | 1 | Fourth Place=2^{3} |

1 ÷ 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:

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