# Octal to Binary Converter

Enter an octal number below to convert it to binary.

## Binary Number:

### Steps to Convert to Binary

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## How to Convert Octal to Binary

Octal and binary numbers are foundational to computing systems. Converting from an octal number to a binary number is very common because base 8 offers a clean way to express three base 2 digits for each base 8 used, making it much easier to read.

Binary numbers, or base 2 numbers, consist of two digits: 0 and 1. Octal, or base 8, numbers consist of 8 digits: 0, 1, 2, 3, 4, 5, 6 & 7.

The base 8 system is often used in legacy computing applications because a single octal digit can represent three binary bits, which are cleanly divisible in 6, 12, 24, and 36-bit computer systems. Most modern computer systems, however, are 16, 32, or 64-bit systems, which are cleanly divisible into base 16 numbers.

Therefore, the hexadecimal system is more commonly used today.

To convert octal to binary, convert each digit to the equivalent binary number. Each octal digit is equal to three binary digits or bits.

### Octal Digit to 3-bit Binary Words

The following table shows the 3-bit word of binary digits for each octal digit.

Octal Digit | Binary Word |
---|---|

0 | 000 |

1 | 001 |

2 | 010 |

3 | 011 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |

After converting each octal digit to a 3-bit word, place the words together to get the final number.

**For example,** let’s convert 730_{8} to binary.

7_{8} = 111_{2}

3_{8} = 011_{2}

0_{8} = 000_{2}

Putting it all together, the final binary value is:

111 011 000

After removing the spaces, you should end up with:

111011000_{2}

## Octal to Binary Conversion Table

The table below shows a list of octal numbers converted to binary.

Octal Number | Binary Number | Decimal Number |
---|---|---|

0 | 0 | 0 |

1 | 1 | 1 |

2 | 10 | 2 |

3 | 11 | 3 |

4 | 100 | 4 |

5 | 101 | 5 |

6 | 110 | 6 |

7 | 111 | 7 |

10 | 1000 | 8 |

11 | 1001 | 9 |

12 | 1010 | 10 |

13 | 1011 | 11 |

14 | 1100 | 12 |

15 | 1101 | 13 |

16 | 1110 | 14 |

17 | 1111 | 15 |

20 | 10000 | 16 |

21 | 10001 | 17 |

22 | 10010 | 18 |

23 | 10011 | 19 |

24 | 10100 | 20 |

25 | 10101 | 21 |

26 | 10110 | 22 |

27 | 10111 | 23 |

30 | 11000 | 24 |

31 | 11001 | 25 |

32 | 11010 | 26 |

33 | 11011 | 27 |

34 | 11100 | 28 |

35 | 11101 | 29 |

36 | 11110 | 30 |

37 | 11111 | 31 |

40 | 100000 | 32 |

100 | 1000000 | 64 |

200 | 10000000 | 128 |

400 | 100000000 | 256 |

1000 | 1000000000 | 512 |

2000 | 10000000000 | 1024 |

4000 | 100000000000 | 2048 |