Author: M Abo Bakar Aslam
8-to-3 Lines Encoder and 3-to-8 Lines Decoder
An 8-to-3 Lines Encoder and 3-to-8 Lines Decoder are widely used combinational circuits for encoding and decoding operations in digital systems.
1. Truth Table - 8-to-3 Lines Encoder
Suppose inputs are A0 to A7 and outputs are Y2, Y1 and Y0.
Total Number of Rows = 2^(number of inputs) = 2⁸ = 256
| A7 | A6 | A5 | A4 | A3 | A2 | A1 | A0 | Y2 | Y1 | Y0 |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
2. Boolean Expression - 8-to-3 Lines Encoder
Y2 = A4 + A5 + A6 + A7
Y1 = A2 + A3 + A6 + A7
Y0 = A1 + A3 + A5 + A7
3. Truth Table - 3-to-8 Lines Decoder
Suppose inputs are Y2, Y1 and Y0 and outputs are A0 to A7.
Total Number of Rows = 2^(number of inputs) = 2³ = 8
| Y2 | Y1 | Y0 | A7 | A6 | A5 | A4 | A3 | A2 | A1 | A0 |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
4. Boolean Expression - 3-to-8 Lines Decoder
A0 = Y2' Y1' Y0'
A1 = Y2' Y1' Y0
A2 = Y2' Y1 Y0'
A3 = Y2' Y1 Y0
A4 = Y2 Y1' Y0'
A5 = Y2 Y1' Y0
A6 = Y2 Y1 Y0'
A7 = Y2 Y1 Y0
5. Circuit Diagram - Encoder and Decoder
Important Note
Basic encoders assume only one input is active at a time. If multiple inputs are active simultaneously, the output may become undefined. This limitation is addressed using priority encoders.