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 9810 into Binary form?
Ans:
| Decimal No. ÷ by 2 | Quotient | Remainder | Places |
|---|---|---|---|
| 98 ÷ 2 | 49 | 0 | First Place=20 |
| 49 ÷ 2 | 24 | 1 | Second Place=21 |
| 24 ÷ 2 | 12 | 0 | Third Place=22 |
| 12 ÷ 2 | 6 | 0 | Fourth Place=23 |
| 6 ÷ 2 | 3 | 0 | Fifth Place=24 |
| 3 ÷ 2 | 1 | 1 | Sixth Place=25 |
| 1 ÷ 2 | 0 | 1 | Seventh 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 | Quotient | Remainder | Places |
|---|---|---|---|
| 164 ÷ 2 | 82 | 0 | First Place=20 |
| 82 ÷ 2 | 41 | 0 | Second Place=21 |
| 41 ÷ 2 | 20 | 1 | Third Place=22 |
| 20 ÷ 2 | 10 | 0 | Fourth Place=23 |
| 10 ÷ 2 | 5 | 0 | Fifth Place=24 |
| 5 ÷ 2 | 2 | 1 | Sixth Place=25 |
| 2 ÷ 2 | 1 | 0 | Seventh Place=26 |
| 1 ÷ 2 | 0 | 1 | Eighth 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 | Quotient | Remainder | Places |
|---|---|---|---|
| 289 ÷ 2 | 144 | 1 | First Place=20 |
| 144 ÷ 2 | 72 | 0 | Second place=21 |
| 72 ÷ 2 | 36 | 0 | Third Place=22 |
| 36 ÷ 2 | 18 | 0 | Fourth Place=23 |
| 18 ÷ 2 | 9 | 0 | Fifth Place=24 |
| 9 ÷ 2 | 4 | 1 | Sixth Place=25 |
| 4 ÷ 2 | 2 | 0 | Seventh Place=26 |
| 2 ÷ 2 | 1 | 0 | Eighth Place=27 |
| 1 ÷ 2 | 0 | 1 | Ninth 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 | Quotient | Remainder(Digit) | Places |
|---|---|---|---|
| 3468 ÷ 2 | 1734 | 0 | First Place=20 |
| 1734 ÷ 2 | 867 | 0 | Second Place=21 |
| 867 ÷ 2 | 433 | 1 | Third Place=22 |
| 433 ÷ 2 | 216 | 1 | Fourth Place=23 |
| 216 ÷ 2 | 108 | 0 | Fifth Place=24 |
| 108 ÷ 2 | 54 | 0 | Sixth Place=25 |
| 54 ÷ 2 | 27 | 0 | Seventh Place=26 |
| 27 ÷ 2 | 13 | 1 | Eighth Place=27 |
| 13 ÷ 2 | 6 | 1 | Ninth Place=28 |
| 6 ÷ 2 | 3 | 0 | Tenth Place=29 |
| 3 ÷ 2 | 1 | 1 | Eleventh Place=210 |
| 1 ÷ 2 | 0 | 1 | Twelfth 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 | Quotient | Remainder(Digit) | Places |
|---|---|---|---|
| 58976 ÷ 2 | 29488 | 0 | First Place=20 |
| 29488 ÷ 2 | 14744 | 0 | Second place=21 |
| 14744 ÷ 2 | 7372 | 0 | Third Place=22 |
| 7372 ÷ 2 | 3686 | 0 | Fourth Place=23 |
| 3686 ÷ 2 | 1843 | 0 | Fifth Place=24 |
| 1843 ÷ 2 | 921 | 1 | Sixth Place=25 |
| 921 ÷ 2 | 460 | 1 | Seventh places=26 |
| 460 ÷ 2 | 230 | 0 | Eighth Places=27 |
| 230 ÷ 2 | 115 | 0 | Ninth Place=28 |
| 115 ÷ 2 | 57 | 1 | Tenth Place=29 |
| 57 ÷ 2 | 28 | 1 | Eleventh Place=210 |
| 28 ÷ 2 | 14 | 0 | Twelfth Place=211 |
| 14 ÷ 2 | 7 | 0 | Thirteenth Place=212 |
| 7 ÷ 2 | 3 | 1 | Fourteen Place=213 |
| 3 ÷2 | 1 | 1 | Fifteen Place=214 |
| 1 ÷ 2 | 0 | 1 | Sixteen 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 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 0.012
Now let move to the other example
Example 7: Convert the decimal number 0.1562510 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 0.001012
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 | Quotient | Remainder | Places |
|---|---|---|---|
| 25 ÷ 2 | 12 | 1 | First Place=20 |
| 12 ÷ 2 | 6 | 0 | Second Place=21 |
| 6 ÷ 2 | 3 | 0 | Third Place=22 |
| 3 ÷ 2 | 1 | 1 | Fourth Place=23 |
| 1 ÷ 2 | 0 | 1 | Fifth 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 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 0.1012
Final Step: Output of 2510 + Output of 0.62510 = (110012 + 0.10110 )
Hence, the final answer is 11001.1012
Conclusion:
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