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# Octal to Gray Code Converter

###### **Updated:** Sep 19, 2018

Octal to Gray Code Converter is used to convert a Octal number into Gray Code format. Use the

Gray Code Converter tool to convert between any number base and gray code.

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**Output:** Gray Code numbers

### Conversion from Octal to Gray Code

A Octal can be converted to Gray Code in three steps:-

Convert the input octal to binary

Take the first bit of the binary input and write it to the output

Repeat the following steps until you reach the end of the input

Take the second bit of the input and XOR it to the previous bit of the input

Write this result to the output. So, `0 + 0 = 0`

, `0 + 1 = 1`

, `1 + 0 = 1`

and `1 + 1 = 0`

.

#### Example Octal to Gray Code Conversion

Let's say your Octal value is `255`

and you want to convert it to it's Gray Code form.

**Step 1: ** Convert the input octal to binary. So, `255`

becomes `10101101`

**Step 2: ** Take the first bit of the binary input and write it to the output. Output is **1**

**Step 3: ** Repeat the steps below until you reach the end of the input- Take the second bit of the input and XOR it to the previous bit of the input.
`1 + 0 = 1`

- Write the result to the output. Output:
`1`**1**

- Take the third bit of the input and XOR it to the previous bit of the input.
`0 + 1 = 1`

- Write the result to the output. Output:
`11`**1**

- Take the fourth bit of the input and XOR it to the previous bit of the input.
`1 + 0 = 1`

- Write the result to the output. Output:
`111`**1**

- Take the fifth bit of the input and XOR it to the previous bit of the input.
`0 + 1 = 1`

- Write the result to the output. Output:
`1111`**1**

- Take the sixth bit of the input and XOR it to the previous bit of the input.
`1 + 1 = 0`

- Write the result to the output. Output:
`11111`**0**

- Take the seventh bit of the input and XOR it to the previous bit.
`1 + 0 = 1`

- Write the result to the output. Output:
`111110`**1**

- Take the eighth (last) bit of the input and XOR it to the previous bit.
`0 + 1 = 1`

- Write the result to the output. Output:
`1111101`**1**

**Step 4: ** So, our final gray code result is: `11111011`

### Gray Code Table

Decimal | Hex | Binary | Gray Code |
---|

0 | 0 | 0000 | 0000 |

1 | 1 | 0001 | 0001 |

2 | 2 | 0010 | 0011 |

3 | 3 | 0011 | 0010 |

4 | 4 | 0100 | 0110 |

5 | 5 | 0101 | 0111 |

6 | 6 | 0110 | 0101 |

7 | 7 | 0111 | 0100 |

8 | 8 | 1000 | 1100 |

9 | 9 | 1001 | 1101 |

10 | a | 1010 | 1111 |

11 | b | 1011 | 1110 |

12 | c | 1100 | 1010 |

13 | d | 1101 | 1011 |

14 | e | 1110 | 1001 |

15 | f | 1111 | 1000 |

### History

**Created: ** Feb 5, 2018

** Online Tool Designed For: ** Windows, OS X, Android, iOS, Linux

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