So, hey guys today we are going to discuss how to convert the octal number into binary. Before we start let take a recap about Binary and Octal number.
Octal Number: The octal number is an 8 base number system that uses the digit 0 to 8(0,1,2,3,4,5,6,7). These are known as Octal numbers. Here, are some examples of octal numbers are 128, 278, 1438, 2768, etc., and many other numbers.
Binary Number: The binary number is a 2 base number system that uses the digit only 0 and 1. These are known as Binary numbers. Here are some examples of binary numbers: 0102, 102, 1012, 100102
For more details about this topic go to this link โComputer Number Systemโ
For better understanding let start with the example.
Example 1: Convert the octal number (10)8 into Binary?
Sol:
Step 1: Firstly we have to convert the given number 108 into a Decimal number. So, letโs see how to convert
= 1 x 81 + 0 x 80
= 810
Step 2: Now, we have to convert the number 810 into a Binary number. Letโs convertโฆ
As In our blog โ How to Convert Decimal Into Binary Number System,โ we discussed that how to convert it to binaryโฆ
| Decimal No. รท by 2 | Quotient | Remainder |
|---|---|---|
| 8 รท 2 | 4 | 0 |
| 4 รท 2 | 2 | 0 |
| 2 รท 2 | 1 | 0 |
| 1 รท 2 | 0 | 1 |
Write all the remainder from downward to the upward manner
=1000
So, Our answer is (1000)2
Hence, the conversion of octal number 108 is (1000)2.
Example 2: Convert the Octal number (74)8 into Binary?
Sol:
Step 1: Firstly we have to convert the given number 748 into a Decimal number. So, letโs see how to convertโฆ
= 7 x 81 + 4 x 80
= 56 + 4
= 6010
Step 2: Now, we have to convert the number 6010 into a Binary number. Letโs convertโฆ
| Decimal No. รท by 2 | Quotient | Remainder |
|---|---|---|
| 60 รท 2 | 30 | 0 |
| 30 รท 2 | 15 | 0 |
| 15 รท 2 | 7 | 1 |
| 7 รท 2 | 3 | 1 |
| 3 รท 2 | 1 | 1 |
| 1 รท 2 | 0 | 1 |
Write all the remainder from downward to the upward manner
= 111100
So, our answer is (111100)2
Hence, the conversion of octal number 748 is (111100)2.
Example 3: Convert the Octal number (531)8 Into Binary?
Sol:
Step 1: Firstly we have to convert the given number 5318 into a Decimal number. So, letโs see how to convertโฆ
= 5 x 82 + 3 x 81 + 1 x 80
= 320 + 24 + 1
= 34510
Step 2: Now, we have to convert the number 34510 into a Binary number. Letโs convertโฆ
| Decimal No. รท by 2 | Quotient | Remainder |
|---|---|---|
| 345 รท 2 | 172 | 1 |
| 172 รท 2 | 86 | 0 |
| 86 รท 2 | 43 | 0 |
| 43 รท 2 | 21 | 1 |
| 21 รท 2 | 10 | 1 |
| 10 รท 2 | 5 | 0 |
| 5 รท 2 | 2 | 1 |
| 2 รท 2 | 1 | 0 |
| 1 รท 2 | 0 | 1 |
Write all the remainder from downward to the upward manner
= 1010110012
So, our answer is (101011001)2
Hence, the conversion of octal number 5318 is (101011001)2.
Example 4: Convert the octal number (1624)8 into Binary?
Sol:
Step 1: Firstly we have to convert the given number 16248 into a Decimal number. So, letโs see how to convertโฆ
= 1 x 83 + 6 x 82 + 2 x 81 + 4 x 80
= 512 + 384 + 16 + 4
= 91610
Step 2: Now, we have to convert the number (916)10 into a Binary number. Letโs convertโฆ
| Decimal No. รท by 2 | Quotient | Remainder |
|---|---|---|
| 916 รท 2 | 458 | 0 |
| 458 รท 2 | 229 | 0 |
| 229 รท 2 | 114 | 1 |
| 114 รท 2 | 57 | 0 |
| 57 รท 2 | 28 | 1 |
| 28 รท 2 | 14 | 0 |
| 14 รท 2 | 7 | 0 |
| 7 รท 2 | 3 | 1 |
| 3 รท 2 | 1 | 1 |
| 1 รท 2 | 0 | 1 |
Write all the remainder from downward to the upward manner
= 1110010100
So, our answer is (1110010100)2.
Hence, the conversion of octal number 9168 is (1110010100)2.
Example 5: Convert the Octal number (3246)8 into Binary?
Sol:
Step 1: Firstly we have to convert the given number 32468 into a Decimal number. So, letโs see how to convertโฆ
= 3 x 83 + 2 x 82 + 4 x 81 + 6 x 80
= 1536 + 128 + 32 + 6
= 170210
Step 2: Now, we have to convert the number (1702)10 into a Binary number. Letโs convertโฆ
| Decimal No. รท by 2 | Quotient | Remainder |
|---|---|---|
| 1702 รท 2 | 815 | 0 |
| 815 รท 2 | 425 | 1 |
| 425 รท 2 | 212 | 1 |
| 212 รท 2 | 106 | 0 |
| 106 รท 2 | 53 | 0 |
| 53 รท 2 | 26 | 1 |
| 26 รท 2 | 13 | 0 |
| 13 รท 2 | 6 | 1 |
| 6 รท 2 | 3 | 0 |
| 3 รท 2 | 1 | 1 |
| 1 รท 2 | 0 | 1 |
Write all the remainder from downward to the upward manner
= 11010100110
So, our answer is (11010100110)2
Hence, the conversion of octal number 17028 is (11010100110)2.
Conclusion:
Today I have told you that how to convert the octal number into a binary number. I hope you liked this blog, If is not then tell me in the comment section about why you donโt like the blog so that I will improve it as soon as possible for you.
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