Hexadecimal to Octal Conversion

Conversion of Hexadecimal To Octal

While understanding the number system, you will come across four different types of number systems. These number systems are mainly - hexadecimal number system, octal number system, decimal number system, and binary number system. It is definitely possible to convert from one decimal system to another number system. How do we do this conversion? The simple steps involved in converting a hexadecimal number to octal numbers are you first convert the hexadecimal number into its equivalent decimal value and then convert this decimal value to octal decimal number. This article has an in-depth explanation of how to convert such numbers. 


What Are Hexadecimal Numbers?

The numbers whose base value is equivalent to 16 are known as hexadecimal numbers. A single number is usually represented by 16 other numbers. It is denoted as n16, where n is any random hexadecimal number.  The 16 digit number can be a combination of numbers as well as alphabets. The numbers used to represent ranges from 0 - 9 and the alphabets range from A - F.


What Are Octal Numbers?

The numbers whose base value is equivalent to 8 are known as hexadecimal numbers. A single number is usually represented by 8 other numbers. It is denoted as n8, where n is any random octal number.  The 8 digit number can be a combination of numbers. The numbers used to represent ranges from 0 - 7. Octal numbers cannot be represented by 8 and 9.


Hexadecimal to Octal Conversion

There are two hex to octal conversion methods. They are:

Method 1

You cannot convert a hexadecimal number to octal decimal number directly. First, you will have to convert the hexadecimal number to its decimal equivalent and then convert the decimal equivalent to octal decimal number. To understand better, follow the steps given below.

  • Note down the given hexadecimal number

  • Count the number of digits and note down the number of digits in the number

  • Multiply each digit with 16x-1, if x is the position of the digit from the right end.

  • Find the sum of the terms after multiplication

  • The result what is obtained is in the equivalent decimal form

  • Divide the obtained decimal number with 8

  • Write down the value of the remainder

  • Repeat step 6 and step 7 with the quotient, until the value of the quotient is zero

  • Note the remainders in reverse order

  • The number that is obtained is the required result.

Method 2

That was method 1. In case you find that difficult, you can also follow the other method to find the octal decimal value of a hexadecimal number. We know that the hexadecimal number comprises of binary digits. In this method, you can combine these binary digits in the pairs of three and you can relate them to the octal numbers. The steps involved in this method are given below.

  • For every given hexadecimal number’s digit, note down the number equivalent to the binary number.  Add 0’s to the left side, if any of the binary equivalents are less than 4 digits.

  • Next, combine the numbers and make the groups of binary digits from right to left, each containing 3 digits. In case there are less than 3 digits in the last group, add 0’s to the group.

  • Find the value equivalent to the octal numbers of each binary group.

Below are the Hexadecimal to Octal Conversion Examples

Question 1: Convert the following hexadecimal number to octal number 2CD16.

Answer:  Given, 

2CD16 is a hexadecimal number.

2 → 0010, C →1100, D → 1101, 

Now you will be grouping them from right to left, each having 3 digits.

001, 011, 001, 101

001→1,  011 →3, 001→1, 101→5

Hence, 2CD16 = 13158


Question 2: Convert the following hexadecimal number to octal number 3EC16.

Answer:  Given, 

3EC16 is a hexadecimal number.

3 → 0010, E → 1110, C →1100, 

Now you will be grouping them from right to left, each having 3 digits.

001, 011, 101, 100

001→1,  011 →3, 101→5, 100→4

Hence, 3EC16 = 13548

Now that you’ve understood the hexadecimal to octal example problems, look at the table given below for easier conversions. 


Hex to Octal Conversion Table


Hexadecimal

Octal

Equivalent Decimal

Equivalent BInary

0

0

0

0

1

1

1

1

2

2

2

10

3

3

3

11

4

4

4

100

5

5

5

101

6

6

6

110

7

7

7

111

8

10

8

1000

9

11

9

1001

A

12

10

1010

B

13

11

1011

C

14

12

1100

D

15

13

1101

E

16

14

1110

F

17

15

1111


Let’s deep-dive into hexadecimal to octal questions.


Solved Examples

Question 1: What is the equivalent form of F216?

Solution 

F216 = ( F × 161 ) + ( 2 × 160 )

= F × 16 + 2 × 1

= 17 × 16 + 2

= 272 + 2

F216 = 272 (Decimal form)


                  8

272

                  8

34        ---- 0       

                  8

4          ---- 2       


4          ---- 4       


The octal number is 4208.

Therefore, F216 = 4208.

FAQ (Frequently Asked Questions)

1) What are Octal Numbers?

The numbers whose base value is equivalent to 8 are known as hexadecimal numbers. A single number is usually represented by 8 other numbers. It is denoted as n8, where n is any random octal number.  The 8 digit number can be a combination of numbers. The numbers used to represent ranges from 0 - 7. Octal numbers cannot be represented by 8 and 9.

2) What are the Steps Involved in Converting a Hexadecimal Number to Octal Number?

The steps involved in converting a hexadecimal number to octal number are:

  • Note down the given hexadecimal number

  • Count the number of digits and note down the number of digits in the number

  • Multiply each digit with 16x-1, if x is the position of the digit from the right end.

  • Find the sum of the terms after multiplication

  • The result what is obtained is in the equivalent decimal form

  • Divide the obtained decimal number with 8

  • Write down the value of the remainder

  • Repeat step 6 and step 7 with the quotient, until the value of the quotient is zero

  • Note the remainders in reverse order

  • The number that is obtained is the required result.