Octal to Binary
Rewrite an octal value in binary by following the base-8 to base-2 relationship.
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Recent Conversions
Conversion Formula
Conversion Examples
Octal to Binary Table
| Octal | Output |
|---|---|
| 7 | 111 |
| 10 | 1000 |
| 17 | 1111 |
| 20 | 10000 |
| 77 | 111111 |
| 100 | 1000000 |
| 377 | 11111111 |
| 755 | 111101101 |
| 1000 | 1000000000 |
| 1777 | 1111111111 |
Popular Conversions
- 7 octal = 111
- 10 octal = 1000
- 17 octal = 1111
- 20 octal = 10000
- 77 octal = 111111
- 100 octal = 1000000
- 377 octal = 11111111
- 755 octal = 111101101
What is Octal and Binary?
Octal
Definition: Octal is a base-8 number system that uses digits 0 through 7.
History/origin: Octal was widely used in early computing because it groups binary digits more compactly.
Current use: It still appears in programming contexts, permissions notation, and number-system teaching.
Binary
Definition: Binary is a base-2 number system that uses only the digits 0 and 1.
History/origin: Binary became fundamental to digital electronics and computing because switches naturally map to two states.
Current use: Binary is used in programming, data representation, logic design, and computer science education.
Related Number System Conversions
These nearby number-system pages help move the same integer into another notation or coded form.
| Related Conversion | Factor or Rule | Formula |
|---|---|---|
| Number to binary | base 2 | write the integer with powers of 2 |
| Number to hex | base 16 | write the integer with powers of 16 |
| Octal to binary | base 8 to base 2 | convert octal to decimal, then decimal to binary |
| Octal to decimal | base 8 to base 10 | sum digit x 8^place |
| Octal to hexadecimal | base 8 to base 16 | convert octal to decimal, then decimal to hex |
| Numbers to Roman numerals | Roman-symbol rules | use I, V, X, L, C, D, and M patterns |
| Number to letter | spreadsheet-style base 26 | A=1, Z=26, AA=27 |
| Number to name | word form | break the number into grouped place values |
Typical Use Cases
Frequently Asked Questions
Q: What digits are allowed in octal?
A: Octal uses only the digits 0 through 7. If an 8 or 9 appears, the input is not a valid octal number.
Q: Why do octal and binary relate so closely?
A: Because 8 equals 2^3, each octal digit lines up neatly with a three-bit binary chunk.
Q: Why does the converter check the raw text instead of just the numeric value?
A: A plain numeric parser would not catch invalid octal digits reliably. The converter checks the full text so only valid base-8 input is accepted.
Q: Can I include spaces in the octal input?
A: The converter trims ordinary spaces, but the actual digits still have to form a valid octal number.
Q: Does the converter support negative octal values?
A: This converter focuses on unsigned practice examples and standard positive octal notation.
Q: When is this useful?
A: It is useful in programming classes, file-permission notes, number-system practice, and technical references that still use octal.