Hello guys, In our todayโs blog, we will see that how can we convert the Octal number Into a decimal number system. Before we starting our blog Letโs 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 **โOctal Numberโ**.

**Examples of Octal Numbers**โ 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 **โDecimal numberโ**

**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 linkย โComputer Number Systemโ

For better understanding let start directly with the exampleโฆ

*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}. *

Thatโs itโฆ

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 letโs see how they** **solveโฆ**

**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.

So, thatโs for todayโs blog guys. We will meet again with the new topic, till then you read our old blog and tell me if I have made any mistake in my content so please tell me in the comment section so that I will fix it as soon as possible. And, also give us your feedback about this website.

Thanks for reading our Blog๐.