Binary to Octal Converter
Convert between binary (base-2) and octal (base-8) number systems with step-by-step conversion process
Number System Converter
Only digits 0 and 1 are allowed
Only digits 0-7 are allowed
Example Conversions
Binary to Octal Examples:
1112=78
10102=128
110012=318
1011102=568
11110002=1708
Octal to Binary Examples:
78=1112
258=101012
648=1101002
1378=10111112
2478=101001112
Binary to Octal Reference Table
OctalBinaryDecimal
00000
10011
20102
30113
41004
51015
61106
71117
Each octal digit corresponds to exactly 3 binary digits
Quick Tips
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Binary uses base 2 (digits 0-1)
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Octal uses base 8 (digits 0-7)
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Group binary digits in sets of 3 from right to left
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Add leading zeros if needed to complete groups
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Each octal digit = exactly 3 binary digits
Understanding Binary and Octal Number Systems
What are Binary and Octal Numbers?
Binary and octal are different number systems that use different sets of symbols to represent numbers. Binary (base-2) uses only digits 0 and 1, while octal (base-8) uses digits 0 through 7.
Why Convert Between Them?
- •Computer programming and digital systems
- •Data representation and storage
- •Network protocols and addressing
- •Educational and mathematical purposes
Conversion Methods
Binary to Octal:
- 1. Group binary digits in sets of 3 from right to left
- 2. Add leading zeros if needed to complete groups
- 3. Convert each 3-bit group to its octal equivalent
- 4. Concatenate the octal digits
Octal to Binary:
- 1. Convert each octal digit to its 3-bit binary equivalent
- 2. Concatenate all binary groups
- 3. Remove leading zeros from the final result
Key Relationship: Each octal digit corresponds to exactly 3 binary digits, making conversion straightforward.