777₈ → decimal — number base conversion
exam standardbase 8 positional expansion
Answer
511
Why this example is worth doing
The largest three-digit octal number, which is 511 in decimal and 1 1111 1111 in binary — nine bits, all ones. Octal survives mainly in Unix file permissions, where those three digits map to read, write and execute for owner, group and other, and the page makes that connection because it is the only place most students will ever meet base eight in practice.
Try your own input in the Binary ⇄ decimal ⇄ hex ⇄ octal. Convert between any two bases, integers and fractions, with the positional working.
How the answer is reached
Base 8 to base 10
Convert 777 from base 8 to base 10. The sign is carried across unchanged; only the magnitude is converted.
| digit | value | weight | weight (base 10) | digit x weight |
|---|---|---|---|---|
| 7 | 7 | 8^2 | 64 | 448 |
| 7 | 7 | 8^1 | 8 | 56 |
| 7 | 7 | 8^0 | 1 | 7 |
| total | 511 |
Integer part: divide by 10 and read the remainders bottom to top.
| n | divide by | quotient | remainder |
|---|---|---|---|
| 511 | 511 ÷ 10 | 51 | 1 |
| 51 | 51 ÷ 10 | 5 | 1 |
| 5 | 5 ÷ 10 | 0 | 5 |
777 (base 8)511 (base 10)