Convert Octal (Base 8) to Binary (Base 2) with step-by-step solution.
01234567Each digit × 8^position:
| Digit | Value | Position | Calculation | Result |
|---|---|---|---|---|
| 2 | 2 | 2 | 2 × 8^2 | 128 |
| 5 | 5 | 1 | 5 × 8^1 | 40 |
| 5 | 5 | 0 | 5 × 8^0 | 5 |
Divide by 2, collect remainders:
| Step | Dividend | ÷ 2 | Quotient | Remainder | Digit |
|---|---|---|---|---|---|
| 1 | 173 | ÷ 2 | 86 | 1 | 1 |
| 2 | 86 | ÷ 2 | 43 | 0 | 0 |
| 3 | 43 | ÷ 2 | 21 | 1 | 1 |
| 4 | 21 | ÷ 2 | 10 | 1 | 1 |
| 5 | 10 | ÷ 2 | 5 | 0 | 0 |
| 6 | 5 | ÷ 2 | 2 | 1 | 1 |
| 7 | 2 | ÷ 2 | 1 | 0 | 0 |
| 8 | 1 | ÷ 2 | 0 | 1 | 1 |
| Decimal | Octal | Binary |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 2 | 10 |
| 3 | 3 | 11 |
| 4 | 4 | 100 |
| 5 | 5 | 101 |
| 6 | 6 | 110 |
| 7 | 7 | 111 |
| 8 | 10 | 1000 |
| 9 | 11 | 1001 |
| 10 | 12 | 1010 |
| 15 | 17 | 1111 |
| 16 | 20 | 10000 |
| 20 | 24 | 10100 |
| 32 | 40 | 100000 |
| Number System | Base | Value |
|---|---|---|
| Binary | 2 | 10101101 |
| Decimal | 10 | 173 |
| Hexadecimal | 16 | AD |
| Ternary | 3 | 20102 |
| Quaternary | 4 | 2231 |
| Quinary | 5 | 1143 |
| Senary | 6 | 445 |
| Septenary | 7 | 335 |
| Duodecimal | 12 | 125 |
| Vigesimal | 20 | 8D |
| Duotrigesimal | 32 | 5D |
| Hexatrigesimal | 36 | 4T |
To convert from Octal (base 8) to Binary (base 2), first convert to decimal, then convert from decimal to Binary.
Used in Unix file permissions. Uses digits: 01234567
Used in computers and digital systems. Uses digits: 01