Binary to Octal Converter
Convert binary numbers to octal with step-by-step explanations and examples.
01
8
01
Binary to Octal Converter
Binary (Base-2)
Valid characters: 01
Octal (Base-8)
Result will appear here
Binary to Octal Conversion
Conversion Method:
Binary to Octal: Direct grouping method (group by 3 digits)
Process:
- Group binary digits from right to left in groups of 3
- Convert each 3-digit group to its octal equivalent (0-7)
- Combine the octal digits to get the final result
Why this works: 2³ = 8, so 3 binary digits represent exactly 1 octal digit
Examples with Step-by-Step Solutions
Binary to Octal Conversion Table
Each group of 3 binary digits converts to 1 octal digit
000₂
↓
0₈
001₂
↓
1₈
010₂
↓
2₈
011₂
↓
3₈
100₂
↓
4₈
101₂
↓
5₈
110₂
↓
6₈
111₂
↓
7₈
Example 1:
(1010)2
=
(12)8
Step-by-Step Solution:
Converting 1010₍2₎ to base 8:
Step 1: Group binary digits from right to left in groups of 3
(Since 2³ = 8, each group of 3 binary digits = 1 octal digit)
Pad with leading zeros: 1010 → 001010
Grouped: 001 | 010
Step 2: Convert each group to octal:
001₂ = 0 × 2² + 0 × 2¹ + 1 × 2⁰ = 0 + 0 + 1 = 1₈
010₂ = 0 × 2² + 1 × 2¹ + 0 × 2⁰ = 0 + 2 + 0 = 2₈
Therefore: 1010₂ = 12₈
Example 2:
(11011)2
=
(33)8
Step-by-Step Solution:
Converting 11011₍2₎ to base 8:
Step 1: Group binary digits from right to left in groups of 3
(Since 2³ = 8, each group of 3 binary digits = 1 octal digit)
Pad with leading zeros: 11011 → 011011
Grouped: 011 | 011
Step 2: Convert each group to octal:
011₂ = 0 × 2² + 1 × 2¹ + 1 × 2⁰ = 0 + 2 + 1 = 3₈
011₂ = 0 × 2² + 1 × 2¹ + 1 × 2⁰ = 0 + 2 + 1 = 3₈
Therefore: 11011₂ = 33₈
Example 3:
(101101)2
=
(55)8
Step-by-Step Solution:
Converting 101101₍2₎ to base 8:
Step 1: Group binary digits from right to left in groups of 3
(Since 2³ = 8, each group of 3 binary digits = 1 octal digit)
Grouped: 101 | 101
Step 2: Convert each group to octal:
101₂ = 1 × 2² + 0 × 2¹ + 1 × 2⁰ = 4 + 0 + 1 = 5₈
101₂ = 1 × 2² + 0 × 2¹ + 1 × 2⁰ = 4 + 0 + 1 = 5₈
Therefore: 101101₂ = 55₈
Example 4:
(1111000)2
=
(170)8
Step-by-Step Solution:
Converting 1111000₍2₎ to base 8:
Step 1: Group binary digits from right to left in groups of 3
(Since 2³ = 8, each group of 3 binary digits = 1 octal digit)
Pad with leading zeros: 1111000 → 001111000
Grouped: 001 | 111 | 000
Step 2: Convert each group to octal:
001₂ = 0 × 2² + 0 × 2¹ + 1 × 2⁰ = 0 + 0 + 1 = 1₈
111₂ = 1 × 2² + 1 × 2¹ + 1 × 2⁰ = 4 + 2 + 1 = 7₈
000₂ = 0 × 2² + 0 × 2¹ + 0 × 2⁰ = 0 + 0 + 0 = 0₈
Therefore: 1111000₂ = 170₈