Octal is a number system that uses a base of 8. This means that there are 8 possible digits that can be used to represent a number in the octal system: 0, 1, 2, 3, 4, 5, 6, and 7.
To convert a number from decimal (base 10) to octal, you can use the following steps:
- Divide the decimal number by 8.
- Write down the remainder.
- Divide the quotient (result of step 1) by 8.
- Write down the remainder.
- Repeat steps 3 and 4 until the quotient is 0.
- Write the remainders in reverse order to get the octal number.
For example, to convert the decimal number 55 to octal:
55 / 8 = 6 remainder 7
6 / 8 = 0 remainder 6
Therefore, 55 in octal is 67.
Here is a table of the first 20 decimal numbers and their octal equivalents:
| Decimal | Octal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 10 |
| 9 | 11 |
| 10 | 12 |
| 11 | 13 |
| 12 | 14 |
| 13 | 15 |
| 14 | 16 |
| 15 | 17 |
| 16 | 20 |
| 17 | 21 |
| 18 | 22 |
| 19 | 23 |
In computer programming, octal is often used to represent sets of bits, where each digit in the octal number represents 3 bits. This is because 2 to the power of 3 (the number of bits represented by each octal digit) is 8, the base of the octal system. However, octal is not as commonly used in modern computing as it was in the past, with hexadecimal (base 16) being the preferred number system for working with binary data.
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