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

**Output:** Gray Code numbers

Convert Gray Code number to Decimal

View Tool### Decimal

Decimal is the numeric system most used by us humans. It consists of the Hindu-Arabic numerals, a set of 10 digits from 0 to 9.

### 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.

### Conversion from Decimal to Gray Code

A Decimal can be converted to Gray Code using these steps:-

- Convert the input decimal 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 Decimal to Gray Code Conversion

Let's say your Decimal value is `173`

, and you want to convert it to its gray code form.

**Step 1:**Convert the input decimal to binary. So,`173`

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**

- Take the second bit of the input and XOR it to the previous bit of the input.
**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

- Feb 5, 2018
- Tool Launched

## Comments 1

## George Plousos Copy Link

Hi,

I was working in a different mathematical field. Unintentionally, I discovered two ways to convert numbers to Gray code. From right to left: I make the divisions of 173 with the numbers 2,4,8,16,32, ..., 256. I round each quotient to the nearest integer. I am writing this integer down from the corresponding fraction. If this integer is even, then I write below this digit 0, otherwise I write the digit 1. These digits form the Gray Code of 173:

173

_____________________________

256 128 64 32 16 8 4 2

1 1 3 5 11 22 43 87

1 1 1 1 1 0 1 1

Faster method. I can convert all numbers that have equal lengths of digits in the binary system to Gray codes. I do this without turning any number into binary. Here I find it difficult to present this method because it contains graphs, but you can find this here:

http://viXra.org/abs/2004.0456?ref=11278286