Convert Hexadecimal To Octal

In the number system, we come across four different types of the number system, i.e, hexadecimal, octal, decimal and binary. The conversion of these numbers from one form to another is possible. To convert hexadecimal to octal numbers, we have to first understand both the types of number systems.

What are Hexadecimal Numbers?

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

Example: (AB2)16, (98D1)16, (AFD)16

What are Octal Numbers?

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

Example: (112)8, (275)8,(45)8

Hexadecimal to Octal Conversion

Conversion of hexadecimal to octal cannot be done directly. Firstly we need to convert hexadecimal into its equivalent decimal number then decimal to octal. Follow the steps below to understand the process.

  • Consider the given hexadecimal number
  • First count the number of digits in the number
  • If n is the position of the digit from the right end then multiply each digit with 16n-1
  • Add the terms after multiplication
  • Resultant is the equivalent decimal form
  • Divide the decimal number with 8
  • Note down the remainder
  • Continue step 6 and 7 with the quotient, until the quotient is zero
  • Write the remainders in reverse order
  • The obtained number is the required result.

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

Hexadecimal to Octal Examples

Q.1: Find the equivalent octal form of C116.

Solution: Given, a hexadecimal number is C1

C116 = (C × 161) + (1 × 160)

= C × 16 + 1 × 1

=12 × 16 + 1

= 192 + 1

C116 =193 (Decimal form)

Now we have to convert this decimal to octal number;

Hexadecimal to octal example

The octal number is 3018

Hence, C116 = 3018

Q.2: Find the equivalent octal form of F16.

Solution: Given, a hexadecimal number is F.

F16 = (F × 160)

= F × 1

= F

= 15(Decimal form)

Now we have to convert this decimal to equivalent octal number;

Hex to octal conversion

The octal number is 178

Hence, F16 = 178

Q.3: Find the equivalent octal form of 10516

Solution: Given, a hexadecimal number is 105.

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

= 1×256 + 0 × 16 + 5 × 1

=256 + 0 +5

= 261(Decimal form)

Now we have to convert this decimal to equivalent octal;

Decimal to Octal

The octal number is 4058

Hence, 10516 = 4058

Practice Questions

  1. Convert ABCD16 to equivalent octal form.
  2. Convert 91216 to equivalent octal form.
  3. Convert 216 to equivalent octal form.
  4. Convert 1016 to equivalent octal form.