A regular decimal number is the sum of the digits multiplied with 10n.
137 in base 10 is equal to each digit multiplied with its corresponding 10n:
13710 = 1×102+3×101+7×100 = 100+30+7
Octal numbers are read the same way, but each digit counts 8n instead of 10n.
Multiply each digit of the hex number with its corresponding 8n.
37 in base 8 is equal to each digit multiplied with its corresponding 8n:
378 = 3×81+7×80 = 24+7 = 31
7014 in base 8 is equal to each digit multiplied with its corresponding power of 8:
70148 = 7×83+0×82+1×81+4×80= 3584+0+8+4 = 3596
| 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 |
To convert a number from the octal system to the decimal system, follow these steps: Begin with the rightmost digit and multiply it by 8 to the power of zero. Then, move to the left, increasing the power of 8 for each subsequent digit. Finally, add up all these products to obtain the decimal equivalent.