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Hexadecimal numbers are numbers with the base 16.That is it uses 16 different digits to represent the numbers.It is denoted as h16,where h is a hexadecimal number. It may be combination and alphabets and numbers.it uses numbers from 0 to 9 and alphabets A to F.

Example: 1) 22AA     2) 98D1   3) AFD

Octal:

Octal means octadecimal numbers.These numbers uses digits 0 to 7,total 8 digits and its called as octal number system.Octal decimal are numbers with bae 8.It is denoted as o8 and o is an octadecimal number.It does not use digits 8 and 9 to represent a number.

Example: 1)145       2) 567      3) 54

How to Convert Hexadecimal to Octal Number

Below are the steps on how to convert hexadecimal to octal number -

Step 1: Consider the given hexadecimal number

Step 2: First count the number of digits in the number

Step 3: If n is the position of the digit from the right end  then multiply each digit with 16n-1

Step 4: Add the terms after multiplication

Step 5: Resultant is the equivalent decimal form

Step 6: Divide the decimal number with 8

Step 7: Note down the remainder

Step 8:Continue step 6 and 7 with the quitient,untill the quitient is zero

Step 9: Write the remainders in reverse order

Step 10: The obtained number is the required result.

Below are the examples on converting hexadecimal to octal -

Example 1:

Find the equivaleent octal form of C116

Solution:

C116 = (C * 161) + (1 * 160)

= C * 16 + 1 * 1

=12 * 16  + 1

= 192 + 1

=193(Decimal form)

Now we have to conver this decimal to octal

8 | 193

-------
8 | 24  -- 1
-------
8 | 3    -- 0
-------
8 | 0     --3

The octal number is 3018

C116 = 3018

Example 2:

Find the equivaleent octal form of F16

Solution:

F16 = (F * 160)

= F * 1

= F

= 15(Decimal form)

Now we have to conver this decimal to octal

8 | 15

-------
8 | 1  -- 7
-------
8 | 0    -- 1

The octal number is 178

F16 = 178

Example 3:

Find the equivaleent octal form of 10516

Solution:

10516 = (1 * 162) + (0 * 161) + (5 * 160)

= 1*256 + 0 * 16 + 5 * 1

=256 + 0 +5

= 261(Decimal form)

Now we have to conver this decimal to octal

8 | 261

-------
8 | 32  -- 5
-------
8 | 4    -- 0
-------
8 | 0     --4

The octal number is 4058

10516 = 4058

Practice Problems

Example 1: Find the equivaleent octal form of ABCD16

Solution: 125715

Example 2: Find the equivaleent octal form of 91216

Solution: 4422

Example 3: Find the equivaleent octal form of 216

Solution: 2

Example 4: Find the equivaleent octal form of 1016

Solution: 20

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