Octal to Binary Converter
Convert octal numbers to binary with step-by-step explanations and examples.
8
01
8
Octal to Binary Converter
Octal (Base-8)
Valid characters: 01234567
Binary (Base-2)
Result will appear here
Octal to Binary Conversion
Conversion Method:
Octal to Binary: Direct expansion method (each digit to 3 binary)
Process:
- Convert each octal digit to its 3-digit binary equivalent
- Combine all binary groups
- Remove leading zeros if necessary
Examples with Step-by-Step Solutions
Octal to Binary Conversion Table
Each octal digit converts to 3 binary digits
0₈
↓
000₂
1₈
↓
001₂
2₈
↓
010₂
3₈
↓
011₂
4₈
↓
100₂
5₈
↓
101₂
6₈
↓
110₂
7₈
↓
111₂
Example 1:
(12)8
=
(1010)2
Step-by-Step Solution:
Converting 12₍8₎ to base 2:
Step 1: Convert each octal digit to 3 binary digits
(Since 8 = 2³, each octal digit = 3 binary digits)
1₈ = 1₁₀ = 0×2^2 + 0×2^1 + 1×2^0 = 001₂
2₈ = 2₁₀ = 0×2^2 + 1×2^1 + 0×2^0 = 010₂
Step 2: Combine all binary groups:
001 | 010 = 001010
Remove leading zeros: 1010
Therefore: 12₈ = 1010₂
Example 2:
(456)8
=
(100101110)2
Step-by-Step Solution:
Converting 456₍8₎ to base 2:
Step 1: Convert each octal digit to 3 binary digits
(Since 8 = 2³, each octal digit = 3 binary digits)
4₈ = 4₁₀ = 1×2^2 + 0×2^1 + 0×2^0 = 100₂
5₈ = 5₁₀ = 1×2^2 + 0×2^1 + 1×2^0 = 101₂
6₈ = 6₁₀ = 1×2^2 + 1×2^1 + 0×2^0 = 110₂
Step 2: Combine all binary groups:
100 | 101 | 110 = 100101110
Therefore: 456₈ = 100101110₂
Example 3:
(777)8
=
(111111111)2
Step-by-Step Solution:
Converting 777₍8₎ to base 2:
Step 1: Convert each octal digit to 3 binary digits
(Since 8 = 2³, each octal digit = 3 binary digits)
7₈ = 7₁₀ = 1×2^2 + 1×2^1 + 1×2^0 = 111₂
7₈ = 7₁₀ = 1×2^2 + 1×2^1 + 1×2^0 = 111₂
7₈ = 7₁₀ = 1×2^2 + 1×2^1 + 1×2^0 = 111₂
Step 2: Combine all binary groups:
111 | 111 | 111 = 111111111
Therefore: 777₈ = 111111111₂
Example 4:
(123)8
=
(1010011)2
Step-by-Step Solution:
Converting 123₍8₎ to base 2:
Step 1: Convert each octal digit to 3 binary digits
(Since 8 = 2³, each octal digit = 3 binary digits)
1₈ = 1₁₀ = 0×2^2 + 0×2^1 + 1×2^0 = 001₂
2₈ = 2₁₀ = 0×2^2 + 1×2^1 + 0×2^0 = 010₂
3₈ = 3₁₀ = 0×2^2 + 1×2^1 + 1×2^0 = 011₂
Step 2: Combine all binary groups:
001 | 010 | 011 = 001010011
Remove leading zeros: 1010011
Therefore: 123₈ = 1010011₂