1-to-8 Multiplexer

A multiplexer is a combinational circuit that selects one of many inputs and directs it to a single output based on the control signals. In a 1-to-8 multiplexer, there are 8 data inputs, one output, and 3 control input lines.

Working of a 1-to-8 Multiplexer

A 1-to-8 multiplexer has 8 data inputs, labeled D0 to D7, and 3 control input lines, labeled A, B, and C. The control input lines determine which data input is selected and passed to the output.

The control input lines can represent 3 binary values: 000, 001, 010, 011, 100, 101, 110, and 111. These binary values can be used to select one of the 8 data inputs.

Implementation of a 1-to-8 Multiplexer using AND gates

To implement a 1-to-8 multiplexer using AND gates, we need to consider the truth table of the multiplexer and derive the logic expressions for the output based on the control input.

The truth table for a 1-to-8 multiplexer is as follows:

| A | B | C | D0 | D1 | D2 | D3 | D4 | D5 | D6 | D7 | Y |
|---|---|---|----|----|----|----|----|----|----|----|---|
| 0 | 0 | 0 | X | X | X | X | X | X | X | X | Y |
| 0 | 0 | 1 | X | X | X | X | X | X | X | X | Y |
| 0 | 1 | 0 | X | X | X | X | X | X | X | X | Y |
| 0 | 1 | 1 | X | X | X | X | X | X | X | X | Y |
| 1 | 0 | 0 | X | X | X | X | X | X | X | X | Y |
| 1 | 0 | 1 | X | X | X | X | X | X | X | X | Y |
| 1 | 1 | 0 | X | X | X | X | X | X | X | X | Y |
| 1 | 1 | 1 | X | X | X | X | X | X | X | X | Y |

From the truth table, we can derive the logic expressions for the output Y as follows:

Y = (A' * B' * C' * D0) + (A' * B' * C * D1) + (A' * B * C' * D2) + (A' * B * C * D3) + (A * B' * C' * D4) + (A * B' * C * D5) +