Decimal to Octal Converter
Enter a decimal number below to convert it to octal.
Octal Number:
Steps to Convert to Octal
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How to Convert Decimal to Octal
The decimal number system is the system used by many people daily. Also referred to as denary, the decimal number system is a base 10 number system, meaning it is comprised of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 & 9.
Octal numbers, sometimes referred to as oct, are base 8 numbers. The octal number system consists of only eight digits: 0, 1, 2, 3, 4, 5, 6 & 7.
The base 8 system is often used in computing applications because one octal digit evenly represents three binary bits, which are cleanly divisible in 6, 12, 24, and 36-bit computer systems. Since most modern computer systems are 16, 32, or 64-bit systems, and these are cleanly divisible into base 16 numbers, the hexadecimal system is more commonly used today.
Steps to Convert
To convert from decimal to octal, you need to use the successive division method by dividing the decimal number by 8 using long division. There should be a remainder of 0 through 7; write the remainder to the side of the division problem.
Take the result of the first division problem and divide that by 8 again. Like before, there should be a remainder, which you should write to the side of the problem.
Continue this process until the result is 0.
The remainders that you wrote to the side of the division problems are the resulting octal number. The number should be read from the bottom to the top since the least significant digit will be at the top, and the most significant digit will be at the bottom.
For example, let’s convert 472 from base 10 to base 8.
472 ÷ 8 = 59 R 0
59 ÷ 8 = 7 R 3
7 ÷ 8 = 0 R 7
Reading the remainders from the bottom up is 730, so 47210 is equal to 7308.
Want to convert back to decimal to confirm this answer? Try our octal to decimal converter.
Decimal to Octal Conversion Table
The table below shows decimal numbers and the equivalent octal number values.
| Decimal Number | Octal Number |
|---|---|
| 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 |
| 20 | 24 |
| 21 | 25 |
| 22 | 26 |
| 23 | 27 |
| 24 | 30 |
| 25 | 31 |
| 26 | 32 |
| 27 | 33 |
| 28 | 34 |
| 29 | 35 |
| 30 | 36 |
| 31 | 37 |
| 32 | 40 |
| 64 | 100 |
| 128 | 200 |
| 256 | 400 |
| 512 | 1000 |
| 1024 | 2000 |
| 2048 | 4000 |