The octal system is commonly used in computing because of its compatibility with binary, while the decimal system is used in everyday human activities. Converting octal to decimal is essential in areas like computer programming, networking, and system design, where octal numbers need to be interpreted in a more familiar base-10 system.
What is Octal?
The octal number system is a base-8 numeral system that uses eight digits: 0 to 7. Each position in an octal number represents a power of 8, starting from the right.
- Example: 173 (octal)
Each octal digit can be represented as a sum of powers of 8:
1738 = 1×82+7×81+3×80 = 64+56+3 = 12310
What is Decimal?
The decimal number system is a base-10 system that uses ten digits: 0 through 9. It is the most widely used number system in human activities, from counting to finance and engineering.
- Example: 123 (decimal)
Each decimal digit is a sum of powers of 10, making it the most familiar way to express quantities.
Octal to Decimal Conversion
To convert an octal number to decimal, each digit in the octal number is multiplied by the appropriate power of 8, depending on its position. Starting from the rightmost digit, the powers of 8 increase from 0 upwards.
Decimal = (Octal Digit) * 8n
Where n is the position of the digit, starting from 0.
Steps to Convert Octal to Decimal
- Write the octal number and note the position of each digit, starting from 0 on the rightmost digit.
- Multiply each digit by (8^n) based on its position.
- Add all the products to get the decimal equivalent.
Example Conversions
Let’s go through a few examples to better understand how to convert octal numbers to decimal.
Example 1: Convert 173 (octal) to decimal.
- List the powers of 8 for each digit:
- (1 * 82 = 1 * 64 = 64)
- (7 * 81 = 7 * 8 = 56)
- (3 * 80 = 3 * 1 = 3)
- Add the results: (64 + 56 + 3 = 123)
So, 173 (octal) is equal to 123 (decimal).
Example 2: Convert 45 (octal) to decimal.
- List the powers of 8 for each digit:
- (4 * 81 = 4 * 8 = 32)
- (5 * 80 = 5 * 1 = 5)
- Add the results: (32 + 5 = 37)
So, 45 (octal) is equal to 37 (decimal).
Example 3: Convert 377 (octal) to decimal.
- List the powers of 8 for each digit:
- (3 * 82 = 3 * 64 = 192)
- (7 * 81 = 7 * 8 = 56)
- (7 * 80 = 7 * 1 = 7)
- Add the results: (192 + 56 + 7 = 255)
So, 377 (octal) is equal to 255 (decimal).
Octal to Decimal Conversion Table
Here’s a quick reference table showing common octal numbers converted to their decimal equivalents:
Octal | Decimal |
---|---|
1 | 1 |
2 | 2 |
3 | 3 |
4 | 4 |
5 | 5 |
6 | 6 |
7 | 7 |
10 | 8 |
11 | 9 |
12 | 10 |
20 | 16 |
25 | 21 |
50 | 40 |
Online Octal to Decimal Converter
Online tools can make converting octal numbers to decimal fast and easy, especially when working with larger numbers or multiple conversions. These tools are commonly used in computer programming, networking, and electronics.
Steps to Use an Online Converter
- Enter the octal number in the input field.
- Click the “Convert” button.
- The tool will display the equivalent decimal number.