Gray Code to Decimal Converter is used to convert a Gray Code number into Decimal format. Use the Gray Code Converter tool to convert between any number base and gray code.

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

- Take the first bit of the gray code 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 last bit of the output
- Write this result to the output. So,
`0 + 0 = 0`

,`0 + 1 = 1`

,`1 + 0 = 1`

and`1 + 1 = 0`

. - Convert the binary output to decimal

Let's say your Gray Code value is `11111011`

and you want to convert it to it's Decimal form.

**Step 1:**Take the first bit of the gray code input and write it to the output. Output is**1****Step 2:**Repeat the steps below until you reach the end of the input- Take the second bit of the input and XOR it to the last bit of the output.
`1 + 1 = 0`

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

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

- Write the result to the output. Output:
`10`

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

- Write the result to the output. Output:
`101`

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

- Write the result to the output. Output:
`1010`

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

- Write the result to the output. Output:
`10101`

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

- Write the result to the output. Output:
`101011`

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

- Write the result to the output. Output:
`1010110`

**1**

- Take the second bit of the input and XOR it to the last bit of the output.
**Step 3:**So, our binary result is:`10101101`

**Step 4:**Convert the binary output to decimal. So,`10101101`

becomes`173`

Gray Code is an ordering of binary numeral system used for error correction in digital terrestrial television and some cable TV systems.

Decimal is the numeric system most used by us humans. It comprises of 10 digits from 0 to 9.

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 |

- Feb 5, 2018
- Tool Launched