**a] BCD and Ex-3 codes:** In this code decimal digits 0 through 9 are represented (coded) by their natural binary equivalents using four bits and each decimal digit of decimal number is represented by this four bit individually.

Example $(23)_{10}$ is represented as 0010 0011 using BCD code, rather usual $(10111)_2$

Hence BCD representates requires more number of bits to code a decimal number using BCD code than using straight binary code.

This code is also known as 8 – 4 – 2 – 1 code and hence also called as weighted code.

**Ex-3 code:** It is a very useful code in which a decimal number in binary form in such a way that each gray-code number differs from the preceding and the succeeding number by single bit.

- Example: gray code for $(5)_{10} \rightarrow (0111)$

and gray code for $(6)_{10} \rightarrow (0101)$

The above two codes differs by only one bit.

- Gray code is a reflected code and can be constructed using following properties.

1] A 1-bit gray code has two codes 0 and 1 representing decimal nos 0 and 1 respectively.

2] An n-bit ($n \geq$ 2 ) gray code will have first $2^n-1$ gray codes of (n-1) bits written in order with a leading o appended.

3] The last $2^n . 1$ gray codes will be to gray code words of an (n – 1) bit gray code, written in reverse order.

**Example.**

**1] Bit Gray code**

Decimal No. | Gray code |
---|---|

0 | 0 |

1 | 1 |

**2] Bit Gray code**

Decimal No. | Gray code |
---|---|

0 | 00 |

1 | 01 |

2 | 11 |

3 | 10 |