In your study of number systems, you'll encounter four main types: hexadecimal, octal, decimal, and binary. It's entirely feasible to convert between these systems. Converting from hexadecimal to octal involves first converting the hexadecimal number to decimal and then converting that decimal to octal. Here, we'll explore the process of converting hexadecimal numbers to octal.
Introduction
There are four primary number systems: hexadecimal, octal, decimal, and binary. Conversion between these systems involves converting through decimal as an intermediary step. To convert hexadecimal to octal, first convert hexadecimal to decimal, then convert decimal to octal. Understanding the definitions of hexadecimal and octal numbers is crucial before starting this conversion process.
Hexadecimal Numbers Definition
Hexadecimal numbers have a base of 16 and are represented by 16 unique digits, including 0-9 and the letters A-F. They are denoted by the symbol h16, combining both numbers and letters.
Also Read: Conversion of Units
Octal Numbers Definition
Octal numbers have a base value of 8. Each digit in an octal number represents a group of three binary digits (bits). It's denoted as n, where n is any octal digit. Octal digits range from 0 to 7.
Hexadecimal to Octal Numbers 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 |
Method to convert hexadecimal to octal numbers
To convert hexadecimal (base-16) numbers to octal (base-8), you can follow these steps:
- Convert Hexadecimal to Binary: Convert each hexadecimal digit to its 4-bit binary equivalent.
- Group Binary Digits: Group the binary digits into groups of 3, starting from the right (add leading zeros if necessary).
- Convert Binary Groups to Octal: Convert each group of 3 binary digits into its octal equivalent.
- Combine Octal Digits: Combine the octal digits obtained from each group to form the final octal number.
Also Read: Converse of Pythagoras Theorem
Solved Example
Example : Convert 2CD16 into an octal number
Solution : Given, 2CD16 is a hexadecimal number.
20010
C1100
D1101
Now group them right to left, each having 3 digits.
001,011,001,101
0011
0113
0011
1015
Hence, 2CD16 = 13158