How to Convert an Octal Number Into Decimal | Octal to Decimal Conversion

Hello guys, In our today’s blog, we will see that how can we convert the Octal number Into a decimal number system. Before we starting our blog Let’s take a little recap about Octal and Decimal numbers so that you can revise this topic.

Octal Number: Octal numbers is a numbers that it uses the digit 0 to 8(0,1,2,3,4,5,6,7). Which means their base is 8. So, it is called “Octal Number”.

Examples of Octal Numbers– 6₈, 10₈, 27₈, 34₈, 125₈ etc.

Decimal Number: Octal number is a numbers that uses the digit o to 9(0,1,2,3,4,5,6,7,8,9). Which means their base is 10. So, it is called “Decimal number”

Examples of Decimal Numbers: 1₁₀, 8₁₀, 16₁₀, 27₁₀, 156_10, etc.

To get about more details about this topic go to this link “Computer Number System”

For better understanding let start directly with the example…

To convert this number, we have to multiply every place of digit of an octal number with 8 to the power of their corresponding values.

Example: If an octal number has a one-digit number e.g. 5₈, it means it is multiplied by 8⁰ like this 5 x 8⁰ = 5₁₀ because it has only a one-digit number. What, If the octal number has three-digit number like 452₈ then it will multiplied by 8²,8¹,8⁰ like this 4 x 8² + 5 x 8¹ + 2 x 8⁰ = 298₁₀.

That’s it…

Also, go for this article to know how to multiply every place of digit with their corresponding Position/Values: Binary to decimal Conversion.

Example 1: Convert the Octal Number (7)₈ into Decimal?

Sol:

=(7)8

= 7x80

= 7x1

= 7

Hence, the decimal number is (7)10

Example 2: Convert an Octal Number (14)₈ into Decimal?

Sol:

=(14)8

= 1x81 + 4x80

= 1x8 + 4x1

= 12

Hence, the decimal number is (12)10

Example 3: Convert an Octal Number (63)₈ into Decimal?

Sol:

=(63)8

= 6x81 + 3x80

= 6x8 + 3x1

= 48 + 3

= 51

Hence, the decimal number is (51)10

Example 4: Convert an Octal Number (275)₈ into Decimal?

Sol:

=(275)8

= 2x82 + 7x81 + 5x80

= 2x64 + 7x8 + 5x1

= 128 + 56 + 5

= 189

Hence, the decimal number is (186)10

Example 5: Convert an Octal number (756)₈ into Decimal?

Sol:

=(756)8

= 7x82 + 5x81 + 6x80

= 7x64 + 5x8 + 6x1

= 448 + 40 + 6

= 494

Hence, the decimal number is (186)10

Example 6: Convert an Octal Number (1025)₈ into Decimal?

Sol:

=(1025)8

= 1x83 + 0x82 + 2x81 + 5x80

= 1x512 + 0x64 + 2x8 + 5x1

= 512 + 0 + 16 + 5

= 533

Hence, the decimal number is (533)10

Example 7: Convert an Octal Number (6725)₈ into Decimal?

Sol:

=(6725)8

= 6x83 + 7x82 + 2x81 + 5x80

= 6 x 512 + 7 x 64 + 2 x 8 + 5 x 1

= 3072 + 448 + 16 + 5

= 3541

Hence, the decimal number is (3541)10

Now, we are going to solve some decimal point questions and let’s see how they solve…

Example 8: Convert an Octal Number (2.4)₈ into Decimal?

Sol:

=(2.4)8

= 2x80 + 4x8-1

= 2 + 4/8

= (16+4)/8

= 20/8

Hence, the decimal number is (2.5)10

Example 9: Convert an Octal Number (4.32)₈ into Decimal?

Sol:

=(4.32)8

= 4x80 + 3x8-1 + 2x8-2

= 4 x 1 + 3 x 1/8 + 2 x 1/82

= 4 + 3/8 + 2/64

= 4 + 3/8 + 2/32

= (128+12+1)/32

= 141/32 

= 4.40625

Hence, the decimal number is (4.40625)10

Example 10: Convert an Octal Number (52.1)₈ into Decimal?

Sol:

=(52.1)8

= 5x81 + 2x80 + 1x8-1

= 40 + 2 + 1/8

= (320+16+1)/8

= 337/8

= 42.125

Hence, the decimal number is (42.125)10

Example 11: Convert an Octal Number (456.34)₈ into Decimal?

Sol:

=(456.34)8

= 4x82 + 5x81 + 6x80 + 3x8-1 + 4x8-2

= 256 + 40 + 6 + 3/8 + 1/16

= (4096+640+96+6+1)/16

= 302.4375

Hence, the decimal number is (302.4375)10

Example 12: Convert an Octal Number (12.634)₈ into Decimal?

Sol:

=(12.634)8

= 1x81 + 2x80 + 6x8-1 + 3x8-2 + 4x8-3

= 1x8 + 2x1 + 6x1/8 + 3x1/64 + 4x1/512

=  8 + 2 + 6/8 + 3/64 + 1/128

= (1024+256+96+6+1)/128

= 10.8046875

Hence, the decimal number is (10.8046875)10

Conclusion:

I have told you about how to convert the octal number into the Decimal Number. If you have any questions then tell me in the comment section.

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