**Contents**hide

This post we will learn **how to convert octal to decimal** with Illustrated examples showing the conversion steps from a given octal number to an equivalent decimal number.

## Octal to Decimal Converter

## How to Convert Octal to Decimal

**Step 1:** We know that in the octal number system only 8 digits are used (from 0 to 7), so the first thing we do in converting a given number from octal to decimal is representing the octal number in powers of 8 or in other words we can say expressing the octal number with base as 8.

**Step 2:** In the second step, we evaluate all the power of 8 values such as 8^{0} is 1, 8^{1} is 8 etc., and write down each octal digit multiplied with the evaluated power of 8 values.

**Step 3:** We then perform the multiplication of all the weights or octal digits with its respective power of 8 values.

**Step 4:** The final step in converting octal to decimal is adding all the individual values obtained after multiplying each octal digit with its power of 8 values. The sum total gives the decimal equivalent of the given octal number.

Let us see the above conversion with the help of an example for better understanding.

## Octal to Decimal examples

**Example 1: Convert ( 237 )**_{8} Octal to Decimal ( ? )_{10}

_{8}Octal to Decimal ( ? )

_{10}

```
```**= 2 3 7
↑ ↑
MSB LSB**

Step 1: Write down the given octal number and express it as power of 8 starting from right to left for integer values as shown below:

**= 2 x 8**^{2} + 3 x 8^{1} + 7 x 8^{0}

Step 2: Evaluate the Power of 8 values for each octal digit as show below

Where,

- 8
^{0}= 1 - 8
^{1}= 8 - 8
^{2}= 64

**= 2 x 64 + 3 x 8 + 7 x 1**

Step 3: Multiply each power of 8 values with its respective octal digit as shown below:

Where,

- 7 x 1 = 7
- 3 x 8 = 24
- 2 x 64 = 128

Step 4: Add the values obtained after multiplication of each octal digit and the octal weights or power of 8 values.

**= 128 + 24 + 7**

The sum total gives the decimal equivalent[159] of the given octal number[237].

**= 159**

**Therefore ( 2 3 7 )**_{8} = ( 1 5 9 )_{10}

**Example** **2: Convert ( 1000 )**_{8}= ( ? )_{10}

**Example**

_{8}= ( ? )

_{10}

**= 1 0 0 0
↑ ↑
MSB LSB**

**= 1 x 8**^{3} + 0 x 8^{2} + 0 x 8^{1}+ 0 x 8^{0}

**= 1 x 512 + 0 x 64 + 0 x 8 + 0 x 1**

**= 512 + 0 + 0 + 0**

**= 512**

**
Therefore ( 1 0 0 0 )**_{8} = ( 5 1 2 )_{10}

**Example** **3: Convert ( 7777 )**_{8} octal to decimal ( ? )_{10}

**Example**

_{8}octal to decimal ( ? )

_{10}

**= 7 7 7 7
↑ ↑
MSB LSB**

**= 7 x 8**^{3} + 7 x 8^{2} + 7 x 8^{1}+ 7 x 8^{0}

```
```**= 7 x 512 + 7 x 64 + 7 x 8 + 7 x 1**

**= 3584 + 448 + 56 + 7**

**= 4095**

```
```**Therefore ( 7 7 7 7 )**_{8} = ( 4 0 9 5 )_{10}

**Example** **4: Convert ( 2 0 )**_{8}= ( ? )_{10}

**Example**

_{8}= ( ? )

_{10}

**= 2 0**

**= 2 x 8**^{1}+ 0 x 8^{0}

**= 2 x 8 + 0 x 1**

**= 16 + 0 **

**= 16**

```
```**Therefore ( 2 0 )**_{8} = ( 1 6 )_{10}

## Convert Fractional Octal to Decimal fraction

Converting octal to decimal with decimal point i.e when the given octal number has fractional part.

**Solved examples of octal fractions to decimal fraction conversion**

**Example 1: Convert ( 2 1 . 2 1 )**_{8} Octal to decimal with Decimal point ( ? )_{10}

_{8}Octal to decimal with Decimal point ( ? )

_{10}

**= 2 1 . 2 1
↑ ↑
MSD LSD**

**
= 2 x 8**^{1} + 1 x 8^{0} . 2 x 8^{-1} + 1 x 8^{-2 }

**= 2 x 8 + 1 x 1 . 2 x ( 1 / 8 ) + 1 x ( 1 / 64 ) **

**= 16 + 1 . ( 0. 2 5 ) + ( 0 . 0 1 5 6 2 5 ) **

**
= 17 + 0. 265625**

** = 17 . 265625**

**Therefore ( 2 1 . 2 1 )**_{8} = ( 1 7 . 2 6 5 6 2 5 )_{10}

**Example** **2: Convert ( 0.357 )**_{8}= ( ? )_{10}

**Example**

_{8}= ( ? )

_{10}

**= 0 . 3 5 7
↑ ↑
MSD LSD**

**= 0 x 8**^{0} . 3 x 8^{-1} + 5 x 8^{-2} + 7 x 8^{-3}

**= 0 x 1 . 3 x ( 1 / 8 ) + 5 x ( 1 / 64 ) + 7 x ( 1 / 512 ) **

**= 0 . (0. 375) + (0 . 0 7 8 1 2 5 ) + ( 0.013671875 )**

**= 0 . ( 0 . 466796875 )**

**= 0 . 466796875**

** Therefore ( 0 . 3 5 7)**_{8} = ( 0 . 466796875 )_{10}

**Example** **3: Convert octal fraction ( 100.01 )**_{8} to Decimal ( ? )_{10}

**Example**

_{8}to Decimal ( ? )

_{10}

**= 1 0 0 . 0 1
↑ ↑
MSD LSD**

```
```**= 1 x 8**^{2} + 0 x 8^{1} + 0 x 8^{0} . 0 x 8^{-1} + 1 x 8^{-2}

**= 1 x 64 + 0 x 8 + 0 x 1 . 0 x ( 1 / 8 ) + 1 x ( 1 / 64 )**

**= 64 + 0 + 0 . ( 0 ) + ( 0. 015625 )**

**= 64 . ( 0. 015625 ) **

**= 64 . 015625**

```
```**Therefore ( 1 0 0 . 0 1 )**_{8} = ( 64 . 0 1 5 6 2 5 )_{10}