Octal to Binary Converter
Free online tool to instantly convert octal (Base 8) to binary (Base 2). Includes quick conversion tables and step-by-step mathematical explanations.
How to convert Octal to Binary
Converting from Octal (Base 8) toBinary (Base 2) involves positional value evaluation.
Convert Octal to Decimal
Multiply each digit of the octal number by 8 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 Binary
Divide the decimal value repeatedly by 2. Record the remainders after each division. The final binary representation is formed by reading the remainders in reverse order (bottom to top).
Octal to Binary Quick Conversion Table
Common values converted between Octal (Base 8) and Binary (Base 2):
| Decimal (10) | Octal (8) | Binary (2) |
|---|---|---|
| 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 |
| 11 | 13 | 1011 |
| 12 | 14 | 1100 |
| 13 | 15 | 1101 |
| 14 | 16 | 1110 |
| 15 | 17 | 1111 |
| 16 | 20 | 10000 |
| 32 | 40 | 100000 |
| 64 | 100 | 1000000 |
| 100 | 144 | 1100100 |
| 255 | 377 | 11111111 |
Octal to Binary Frequently Asked Questions
Common questions and step-by-step mathematical answers about converting Octal (Base 8) to Binary (Base 2).
1How do you convert octal to binary?↓
Convert each digit into 3 binary bits: 0=000, 1=001, 2=010, 3=011, 4=100, 5=101, 6=110, 7=111. Concatenate the bits.
2What is the method for converting octal to binary?↓
Because 8 = 2³, every octal digit expands directly into a 3-bit binary triplet with zero calculation overhead.
3How do you convert octal to binary manually?↓
Example with 74₈: 7 = 111, 4 = 100 → 111100₂.
4What is 10 in binary from octal?↓
1 = 001, 0 = 000 → 1000₂ (which equals decimal 8).
5Why does each octal digit represent three binary bits?↓
The mathematical power relation 8 = 2³ ensures a direct 1-to-3 bit mapping between octal and binary.
6How do you convert octal fractions to binary?↓
Example: 0.52₈ → 5 = 101, 2 = 010 → 0.101010₂.
7What is the relationship between octal and binary?↓
This direct power-of-2 relationship makes octal a convenient representation for low-level binary data.
8How do you convert large octal numbers to binary?↓
Example: 1753₈ → 1(001) 7(111) 5(101) 3(011) → 1111101011₂.
9Should leading zeros be included in binary results?↓
In pure mathematics, 001000₂ simplifies to 1000₂. In computing, byte alignment may preserve leading zeros.
10How do you calculate binary values from octal numbers?↓
By looking up or calculating the 3-bit value for each digit, the full binary string is constructed immediately.