**Octal-to-Binary Encoder**

An octal-to-binary encoder is a digital circuit that converts an octal input signal into a binary output signal. It takes in three inputs (A2, A1, A0) representing the octal number and produces four outputs (Y3, Y2, Y1, Y0) representing the binary number.

**Logic Diagram**

The logic diagram of an octal-to-binary encoder can be implemented using OR gates, as shown below:

```
_______
A2 --------| |
A1 --------| OR |------ Y3
A0 --------|_______|

_______
A2 --------| |
A1 --------| OR |------ Y2
A0 --------|_______|

_______
A2 --------| |
A1 --------| OR |------ Y1
A0 --------|_______|

_______
A2 --------| |
A1 --------| OR |------ Y0
A0 --------|_______|
```

**Explanation**

- The octal input signal has three bits (A2, A1, A0), representing the numbers 0 to 7.
- The binary output signal has four bits (Y3, Y2, Y1, Y0), representing the numbers 0 to 15.
- Each output bit is produced by a separate OR gate.
- The inputs A2, A1, and A0 are connected to each OR gate as shown in the logic diagram.
- The output of each OR gate will be high (1) if any of its inputs are high (1).
- Therefore, the OR gates perform a logical OR operation on the input bits and produce the corresponding output bits.

**Number of OR Gates**

To implement an octal-to-binary encoder, we need one OR gate for each output bit. Since there are four output bits (Y3, Y2, Y1, Y0), we need a total of four OR gates.

Hence, the correct answer is option A) 3.