# (e) Explain the functioning of a 3 × 8 decoder with the help of logic diagram and example input.

, ,

A 3-to-8 decoder is a digital circuit that takes a 3-bit binary input and activates one of the eight output lines based on the input code. Each output line corresponds to one of the possible input combinations.

Functioning of a 3 × 8 Decoder:

Logic Diagram:

A 3-to-8 decoder typically consists of three inputs (A, B, C) and eight outputs (Y0 to Y7). The number of outputs is 2^n, where n is the number of input lines.

```

+----+          +----+

A |    | Y0       0 |    |

B |    | Y1       1 |    |

C |    | Y2   =>  2 |    |

|    | Y3   =>  3 |    |

|    | Y4   =>  4 |    |

|    | Y5   =>  5 |    |

|    | Y6   =>  6 |    |

|    | Y7       7 |    |

+----+             +----+

```

Example Input:

Let's consider an example with the input code A=1, B=0, C=1.

Truth Table:

```

| A | B | C | Y0 | Y1 | Y2 | Y3 | Y4 | Y5 | Y6 | Y7 |

|---|---|---|----|----|----|----|----|----|----|----|

| 1 | 0 | 1 | 0  | 1  | 0  | 0  | 0  | 0  | 0  | 0  |

```

Explanation:

- The binary input code is 101.

- The corresponding output line Y5 is activated (Y5 = 1), and all other output lines are deactivated (Y0 to Y4 and Y6 to Y7 = 0).

In summary, a 3-to-8 decoder decodes a 3-bit binary input into one of eight possible output lines based on the binary input code. Each output line corresponds to a unique input combination, and only the activated output line corresponds to the input code applied.