Before going to hexadecimal to octal conversion we have to know about hexadecimal and octal number systems. If you already have known about them then you can continue to convert bellow of this post.

However, Hexadecimal is the 16 based very important number system for computer. If you have the experience to work with different color code, then it is sure that you have used hexadecimal color code.

HTML (Hyper Text Markup Language) supports hexadecimal color code. But today it is not our topic to discuss. Here we will convert a number from hexadecimal to octal only.

Octal number is also very important number system which has a base of 8 and we use 0 to 7 as octal digits where we can use both 0 to 9 and A, B, C, D, E, F as hexadecimal digits.

However, we already have discussed about basic 4 number system and you can see from here.

Number system and conversion of binary, octal, decimal and hexadecimal.

Now, let’s come back to the topics.

To convert a number from hexadecimal to octal we have to know some rules. We know that hexadecimal is the 16 based number system where octal is the 8 based.

In this article we will learn to convert a number from hexadecimal to octal. We will use two separate rule for converting integer part and fraction part of a hexadecimal number. Let’s see these rules.

- Replace each hexadecimal digit by their equivalent binary number and write them side by side as their hexadecimal order.
- Take every 3 bit from right to left and fill up by taking zeros if there is not available digit at the left to consist 3 bits.
- Replace every 3 bit by their equivalent octal value.

Don’t be frustrated to see these rules. This might looks like very hard if you see these rules for the first time. But you will be clear to see the example conversion bellow. Let’s see this.

**Example**: Conversion of (E5F)_{16} to equivalent octal number

We will use above rules for converting this integer number from hexadecimal to octal. See the figure to understand the conversion.

At first we will write the equivalent binary number of given hexadecimal number which will be 4 bit for every hexadecimal digits. Then we will take each 3 bits and write their equivalence in octal number.

However, we can ignore or take necessary **zeros at left** at the time of our conversion from hexadecimal to octal. The number 84 and 084 has the same meaning and this is applicable for both the hexadecimal and octal number as well.

You can convert any number from hexadecimal to octal by these rules. Now it is your time to practice more but it is not the end.

We have to learn a few more rules for converting a fraction number from hexadecimal to octal. Let’s learn the given rules for this purpose.

### Rules for fraction number

- Replace each hexadecimal digit by their equivalent binary number and write them side by side as their hexadecimal order.
- Take every 3 bit from left to right and fill up by taking zeros if there is not available digit at the right to consist 3 bits.
- Replace every 3 bit by their equivalent hexadecimal value.

Similarly as the integer rules, we will implement these rules in the given example conversion bellow. So, try to understand through the following conversion.

**Example**: Conversion of (0.7C9)_{16} to equivalent octal number.

By the similar way of integer portion, here also we will write the equivalent binary digits first then we will take every 3 digits of binary number and convert them to octal number. Look bellow.

As like as the same process of decimal number we can ignore **zero at right**, when we convert a fraction number from hexadecimal to octal.

I hope, it is now clear to you that how can we convert a number from hexadecimal to octal using several rules. Now, you can convert a full number from hexadecimal to octal using these rules.

Now, we will see a full example to convert a number from hexadecimal to octal. This will help you to understand the conversion. If you have any doubt still now, then see the example.

**Example**: Conversion of (A4B.59E)_{16} to equivalent octal number

The given hexadecimal number is A4B.59E and we have to convert it to equivalent octal number. For this conversion we can convert the whole number by a single rule which will apply at both it’s integer part and fraction part.

Here also we will ignore or take necessary zeros at left side of integer and right side of fraction part for our conversion purpose only.

So, we have got the equivalent octal number is **(5113.2636) _{8} **. Now, you should try some other number to get the clear idea about this conversion. So, try this.

So, your learning journey for converting from hexadecimal to octal is finish here. But you should practice taking different hexadecimal number to become master at conversion.

So guys, I hope that you have not any doubt about the conversion from hexadecimal to octal now. I already have discussed almost everything about that. Hope, this was helpful for you.

Please tell us your opinion or any question about hexadecimal to octal number conversion in the comment box bellow. This will inspire us to go ahead. Thanks for remaining with us.

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