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Octal and decimal are two different numeral systems used to represent numbers. These systems are used for counting, arithmetic operations, and other mathematical tasks. Here’s a brief overview of each system:
Decimal
The decimal system, also known as the base-10 system, is the most common numeral system used by humans. It uses ten symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent numbers. Each digit’s position in a decimal number represents a power of 10.
Octal
The octal system, also known as the base-8 system, uses eight symbols (0, 1, 2, 3, 4, 5, 6, and 7) to represent numbers. Each digit’s position in an octal number represents a power of 8. For instance, in the number 235 in octal, the “2” represents 2 * 8^2, the “3” represents 3 * 8^1, and the “5” represents 5 * 8^0. Adding these components gives you the total value of 173 in decimal.
How to convert octal to decimal
To convert a number from octal to decimal, you can follow these steps:
- Write down the octal number.
- Identify the digits in the octal number from left to right.
- Assign a power of 8 to each digit based on its position, starting with 0 for the rightmost digit and increasing by 1 for each subsequent digit.
- Multiply each digit by 8 raised to its corresponding power and sum up the results.
Example: Convert the octal number 347 to decimal.
Ans. Octal number: 347
Digits: 3, 4, 7
Now, assign powers of 8 to each digit:
- The rightmost digit (7) has a power of 8^0 = 1.
- The middle digit (4) has a power of 8^1 = 8.
- The leftmost digit (3) has a power of 8^2 = 64.
- Calculate the decimal value of each digit:
7 * 8^0 = 7 * 1 = 7
4 * 8^1 = 4 * 8 = 32
3 * 8^2 = 3 * 64 = 192
Now, sum up the results:
7 + 32 + 192 = 231
So, the octal number 347 is equivalent to the decimal number 231.
Also Read: Octal to binary converter
Octal to decimal conversion table
| Octal
base 8 |
Decimal base 10 |
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 10 | 8 |
| 11 | 9 |
| 12 | 10 |
| 13 | 11 |
| 14 | 12 |
| 15 | 13 |
| 16 | 14 |
| 17 | 15 |
| 20 | 16 |
| 30 | 24 |
| 40 | 32 |
| 50 | 40 |
| 60 | 48 |
| 70 | 56 |
| 100 | 64 |
FAQs on Octal to Decimal Converter
How do you convert octal to decimal?
o convert octal to decimal: Write down the octal number. Assign powers of 8 to each digit from right to left (starting with 8^0 for the rightmost digit). Multiply each digit by its corresponding power of 8. Sum up the results to get the decimal equivalent.
What is 7 in octal when converted to decimal?
The octal number 7 is equivalent to the decimal number 7.
What is the decimal equivalent of the octal number 123?
To convert octal 123 to decimal: 3 * 8^0 = 3 * 1 = 3 2 * 8^1 = 2 * 8 = 16 1 * 8^2 = 1 * 64 = 64 Adding these results: 3 + 16 + 64 = 83. So, octal 123 is decimal 83.
Convert the octal number 139 to decimal.
To convert octal 139 to decimal: 9 * 8^0 = 9 * 1 = 9 3 * 8^1 = 3 * 8 = 24 1 * 8^2 = 1 * 64 = 64 Adding these results: 9 + 24 + 64 = 97. Therefore, octal 139 is decimal 97.
How do you convert the octal number 136 to decimal?
To convert octal 136 to decimal: 6 * 8^0 = 6 * 1 = 6 3 * 8^1 = 3 * 8 = 24 1 * 8^2 = 1 * 64 = 64 Adding these results: 6 + 24 + 64 = 94. Thus, octal 136 is equivalent to decimal 94.
What is the decimal representation of the octal number 210?
To convert octal 210 to decimal: 0 * 8^0 = 0 * 1 = 0 1 * 8^1 = 1 * 8 = 8 2 * 8^2 = 2 * 64 = 128 Adding these results: 0 + 8 + 128 = 136. Therefore, octal 210 is equal to decimal 136.
