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

**Output:** Binary numbers

Convert Binary number to Gray Code

View Tool### Gray Code

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

### Binary

Binary is the numeric system of computers. Computers are so dumb they only understand 0s and 1s. Binary numbers have a base of 2.

### Conversion from Gray Code to Binary

A Gray Code can be converted to Binary using these 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`

.

#### Example Gray Code to Binary Conversion

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

, and you want to convert it to its binary 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`

### 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

- Feb 5, 2018
- Tool Launched

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