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.

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