Binary to Octal Converter
Free online tool to instantly convert binary (Base 2) to octal (Base 8). Includes quick conversion tables and step-by-step mathematical explanations.
How to convert Binary to Octal
Converting from Binary (Base 2) toOctal (Base 8) involves positional value evaluation.
Convert Binary to Decimal
Multiply each digit of the binary number by 2 raised to the power of its position index (starting from position 0 on the right). Sum all products together to obtain the decimal equivalent.
Convert Decimal to Octal
Divide the decimal value repeatedly by 8. Record the remainders after each division. The final octal representation is formed by reading the remainders in reverse order (bottom to top).
Binary to Octal Quick Conversion Table
Common values converted between Binary (Base 2) and Octal (Base 8):
| Decimal (10) | Binary (2) | Octal (8) |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 10 | 2 |
| 3 | 11 | 3 |
| 4 | 100 | 4 |
| 5 | 101 | 5 |
| 6 | 110 | 6 |
| 7 | 111 | 7 |
| 8 | 1000 | 10 |
| 9 | 1001 | 11 |
| 10 | 1010 | 12 |
| 11 | 1011 | 13 |
| 12 | 1100 | 14 |
| 13 | 1101 | 15 |
| 14 | 1110 | 16 |
| 15 | 1111 | 17 |
| 16 | 10000 | 20 |
| 32 | 100000 | 40 |
| 64 | 1000000 | 100 |
| 100 | 1100100 | 144 |
| 255 | 11111111 | 377 |
Binary to Octal Frequently Asked Questions
Common questions and step-by-step mathematical answers about converting Binary (Base 2) to Octal (Base 8).
1How do you convert binary to octal?↓
Split bits into triplets from right to left, pad the leftmost group with leading 0s if needed, and map each triplet (000=0 to 111=7).
2What is the method for converting binary to octal?↓
Group binary digits in 3s from the binary point, pad with 0s, and convert directly without calculating intermediate decimal numbers.
3How do you convert binary to octal manually?↓
Example with 110101₂: Group as [110] [101] → 110₂ = 6, 101₂ = 5 → 65₈.
4What is 1010 in octal?↓
Group 1010 as [001] [010] → 001₂ = 1, 010₂ = 2 → 12₈.
5How do you group binary digits for octal conversion?↓
For integers: start at the right. For fractional bits: start at the binary point and group to the right, padding trailing zeros if necessary.
6Why are binary digits grouped in sets of three for octal?↓
3 bits produce 2³ = 8 distinct permutations (000 through 111), corresponding 1:1 with octal digits 0–7.
7How do you convert binary fractions to octal?↓
Example: 0.1101₂ → [110] [100] → 0.64₈.
8What is the relationship between binary and octal?↓
Octal is often used in computer systems (like Unix file permissions) to represent binary masks cleanly.
9Can binary numbers with leading zeros be converted to octal?↓
001010₂ has the same value as 1010₂ (both equal 12₈).
10How do you calculate octal from a binary number?↓
Each 3-bit group [b₂ b₁ b₀] evaluates directly as 4b₂ + 2b₁ + b₀ in octal.