How to Convert Decimal Into Binary Number System

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.

Copyrighted to computerstudypoint.com

Now, lets do some examples:

Example 1: Convert the decimal number 9810 into Binary form?

Ans:

Decimal No.
÷ by 2
QuotientRemainderPlaces
98 ÷ 2490First Place=20
49 ÷ 2241Second Place=21
24 ÷ 2120Third Place=22
12 ÷ 260Fourth Place=23
6 ÷ 230Fifth Place=24
3 ÷ 211Sixth Place=25
1 ÷ 201Seventh Place=26

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 16410 into binary form?

Ans:

Decimal no.
÷ by 2
QuotientRemainderPlaces
164 ÷ 2820First Place=20
82 ÷ 2410Second Place=21
41 ÷ 2201Third Place=22
20 ÷ 2100Fourth Place=23
10 ÷ 250Fifth Place=24
5 ÷ 221Sixth Place=25
2 ÷ 210Seventh Place=26
1 ÷ 201Eighth Place=27

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 28910 into binary form?

Ans:

Decimal no.
÷ by 2
QuotientRemainderPlaces
289 ÷ 21441First Place=20
144 ÷ 2720Second place=21
72 ÷ 2360Third Place=22
36 ÷ 2180Fourth Place=23
18 ÷ 290Fifth Place=24
9 ÷ 241Sixth Place=25
4 ÷ 220Seventh Place=26
2 ÷ 210Eighth Place=27
1 ÷ 201Ninth Place=28

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 346810 into binary form?

Ans:

Decimal no.
÷ by 2
QuotientRemainder(Digit)Places
3468 ÷ 217340First Place=20
1734 ÷ 28670Second Place=21
867 ÷ 24331Third Place=22
433 ÷ 22161Fourth Place=23
216 ÷ 21080Fifth Place=24
108 ÷ 2540Sixth Place=25
54 ÷ 2270Seventh Place=26
27 ÷ 2131Eighth Place=27
13 ÷ 261Ninth Place=28
6 ÷ 230Tenth Place=29
3 ÷ 211Eleventh Place=210
1 ÷ 201Twelfth Place=211

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 5897610 into binary form?

Ans:

Decimal no.
÷ by 2
QuotientRemainder(Digit)Places
58976 ÷ 2294880First Place=20
29488 ÷ 2147440Second place=21
14744 ÷ 273720Third Place=22
7372 ÷ 236860Fourth Place=23
3686 ÷ 218430Fifth Place=24
1843 ÷ 29211Sixth Place=25
921 ÷ 24601Seventh places=26
460 ÷ 22300Eighth Places=27
230 ÷ 21150Ninth Place=28
115 ÷ 2571Tenth Place=29
57 ÷ 2281Eleventh Place=210
28 ÷ 2140Twelfth Place=211
14 ÷ 270Thirteenth Place=212
7 ÷ 231Fourteen Place=213
3 ÷211Fifteen Place=214
1 ÷ 201Sixteen Place=215

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 0.2510 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 2Result
0.25 x 2= 0.50
0.5 x 2= 1.01

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

=Hence, our final answer is 0.012

Now let move to the other example

Example 7: Convert the decimal number 0.1562510 into binary form?

Ans:

Decimal no. x by 2Result
0.15625 x 2= 0.31250
0.3125 x 2= 0.6250
0.625 x 2= 1.251
0.25 x 2= 0.50
0.5x 2 = 11

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

Hence, the binary number is 0.001012

Example 8: Convert the decimal number 25.62510 into binary form.

Ans: In this number 25.625, we have to solve firstly 2510 into binary in and then after 0.62510. After that, we will sum the output of 2510 and 0.62510.

Example = (output of 25 +output of 0.625)= Final answer = (…………)2

Step1: For now, we have to solve 2510 into binary

Decimal no.
÷ by 2
QuotientRemainderPlaces
25 ÷ 2121First Place=20
12 ÷ 260Second Place=21
6 ÷ 230Third Place=22
3 ÷ 211Fourth Place=23
1 ÷ 201Fifth Place=24

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 0.62510 into binary

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

Decimal no. x by 2Resultant integer part (R)
0.625 x 2= 1.251
0.25 x 2= 0.50
0.5 x 2= 11

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

=Hence, the binary no. is 0.1012

Final Step: Output of 2510 + Output of 0.62510 = (110012 + 0.10110 )

Hence, the final answer is 11001.1012

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 😊

Also, Read these Related Articles

Spread the love

Add a Comment

Your email address will not be published.

Difference Between Bit and Byte? What is DataBase And Its Uses Types of Computer System Evolution of Computer What is Computer System ?