How to Convert octal into Binary Number System | Number System

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 “Computer Number System”

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, let’s 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. Let’s convert…

As In our blog ” How to Convert Decimal Into Binary Number System,” we discussed that how to convert it to binary…

Decimal No.
÷ by 2
QuotientRemainder
8 ÷ 240
4 ÷ 220
2 ÷ 210
1 ÷ 201

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, let’s see how to convert…

= 7 x 81 + 4 x 80

= 56 + 4

= 6010

Step 2: Now, we have to convert the number 6010 into a Binary number. Let’s convert…

Decimal No.
÷ by 2
Quotient Remainder
60 ÷ 2300
30 ÷ 2150
15 ÷ 271
7 ÷ 231
3 ÷ 211
1 ÷ 201

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, let’s see how to convert…

= 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. Let’s convert…

Decimal No.
÷ by 2
Quotient Remainder
345 ÷ 21721
172 ÷ 2860
86 ÷ 2430
43 ÷ 2211
21 ÷ 2101
10 ÷ 250
5 ÷ 221
2 ÷ 210
1 ÷ 201

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, let’s see how to convert…

= 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. Let’s convert…

Decimal No.
÷ by 2
Quotient Remainder
916 ÷ 24580
458 ÷ 22290
229 ÷ 21141
114 ÷ 2570
57 ÷ 2281
28 ÷ 2140
14 ÷ 270
7 ÷ 231
3 ÷ 211
1 ÷ 201

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, let’s see how to convert…

= 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. Let’s convert…

Decimal No.
÷ by 2
Quotient Remainder
1702 ÷ 28150
815 ÷ 24251
425 ÷ 22121
212 ÷ 21060
106 ÷ 2530
53 ÷ 2261
26 ÷ 2130
13 ÷ 261
6 ÷ 230
3 ÷ 211
1 ÷ 201

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 don’t like the blog so that I will improve it as soon as possible for you.

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