**binary to gray code**:

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## Binary number

Binary numbering system uses only two symbols 0 and 1. Each digits of a binary number is referred to as *bits*. Binary system is also known as *base -2 system*. Each digit is represented by the increasing *power of 2* from the LSB (Least Significant Bit). Binary system is the heart of digital electronics and is used for information flow. In digital electronics, 0 and 1 are used to denote logic states, high and low. Arithmetic operations are also possible in binary system.

## Gray code

Gray code, also known as *reflected binary code*, is a code having digits 0 and 1. Gray code do not have place value for its digits. Any successive codes in Gray code system have only one bit changes.

## Binary to gray code conversion can be made easy with an example:

### Let us convert a binary value of 1010 to gray code:

Step 1: The MSB (Most Significant Bit) of a gray code and binary code will be the same.

Step 2: The next digit of gray code will be the EXOR of the MSB and the digit right to the MSB of the binary code.

Step 3: Similarly EXOR the digit in place and the previous digit of binary code to obtain the next digit of gray code.

Step 4: Repeat the previous step till the LSB of gray code is found.

### Read More: How to convert a binary number to a gray code

## Decimal to binary to gray conversion table

Decimal | Binary | Gray |
---|---|---|

0 | 0000 | 0000 |

1 | 0001 | 0001 |

2 | 0010 | 0011 |

3 | 0011 | 0010 |

4 | 0100 | 0110 |

5 | 0101 | 0111 |

6 | 0110 | 0101 |

7 | 0111 | 0100 |

8 | 1000 | 1100 |

9 | 1001 | 1101 |

10 | 1010 | 1111 |

11 | 1011 | 1110 |

12 | 1100 | 1010 |

13 | 1101 | 1011 |

14 | 1110 | 1001 |

15 | 1111 | 1000 |

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