Sep 19, 2018 0 Comments

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.

Background Information

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

A Gray Code can be converted to Binary 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`

.

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

and you want to convert it to it's 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`

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

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