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**– 6_{8}, 10_{8}, 27_{8}, 34_{8}, 125_{8} 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:** 1_{10}, 8_{10}, 16_{10}, 27_{10}, 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. 5 _{8}, it means it is multiplied by 8^{0} like this 5 x 8^{0} = 5_{10} because it has only a one-digit number. What, If the octal number has three-digit number like 452_{8} then it will multiplied by 8^{2},8^{1},8^{0} like this 4 x 8^{2} + 5 x 8^{1} + 2 x 8^{0} = 298_{10}. *

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}= 7x8^{0}= 7x1 = 7 Hence, the decimal number is(7)_{10}

**Example 2: **Convert an Octal Number **(14) _{8}** into Decimal?

**Sol:**

=(14)_{8}= 1x8^{1}+ 4x8^{0}= 1x8 + 4x1 = 12 Hence, the decimal number is(12)_{10}

**Example 3: **Convert an Octal Number **(63) _{8}** into Decimal?

**Sol:**

=(63)_{8}= 6x8^{1}+ 3x8^{0}= 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}= 2x8^{2}+ 7x8^{1}+ 5x8^{0}= 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}= 7x8^{2}+ 5x8^{1}+ 6x8^{0}= 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}= 1x8^{3}+ 0x8^{2}+ 2x8^{1}+ 5x8^{0}= 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}= 6x8^{3}+ 7x8^{2}+ 2x8^{1}+ 5x8^{0}= 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}= 2x8^{0}+ 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}= 4x8^{0}+ 3x8^{-1}+ 2x8^{-2}= 4 x 1 + 3 x 1/8 + 2 x 1/8^{2}= 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}= 5x8^{1}+ 2x8^{0}+ 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}= 4x8^{2}+ 5x8^{1}+ 6x8^{0}+ 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}= 1x8^{1}+ 2x8^{0}+ 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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