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
Frequently Asked Questions
Ans. Convert hexadecimal to octal by first converting hexadecimal to binary, grouping binary digits into sets of three, and then converting each set to octal.
Ans. Convert octal to hexadecimal by first converting octal to binary, then grouping binary digits into sets of four, and finally converting each set to hexadecimal.
Ans. To convert 1D7F₁₆ to octal, first convert it to binary (0001 1101 0111 1111), group binary digits into sets of three (001 110 101 111 111), and then convert each group to octal (175₈).
Ans. Convert 1056₁₆ to octal by first converting it to binary (0001 0000 0101 0110), grouping binary digits into sets of three (001 000 001 010 110), and then converting each group to octal (206₈).