Design an 8-to-1 Line Multiplexer Using a 3-to-8 Line Decoder and AND/OR Gates

Designing a multiplexer can seem complex, but using a 3-to-8 line decoder combined with AND and OR gates simplifies the process significantly. This guide will walk you through the required components and design steps to create an 8-to-1 line multiplexer (MUX) using these basic logic gates.

Components Required

3-to-8 Line Decoder: This decodes 3 select lines to activate one of 8 output lines. 8 2-input AND Gates: Each AND gate combines the decoder's output with a data input. 8-input OR Gate: This combines the outputs of the AND gates to produce the final output.

Design Steps

Inputs and Select Lines

The data inputs are denoted as D0 to D7, with the select lines being S2 S1 S0. These 3 bits will select one of the 8 inputs.

3-to-8 Decoder

The decoder takes 3 inputs S2 S1 S0 and outputs 8 lines Y0 to Y7. Each output Y_i is HIGH (1) when the corresponding input D_i is selected by the select lines.

AND Gates

Each AND gate has two inputs: one from the corresponding output of the decoder and the other from the data input. Here is how the connections are made:

AND0: Y0 and D0 → Output O0 AND1: Y1 and D1 → Output O1 AND2: Y2 and D2 → Output O2 AND3: Y3 and D3 → Output O3 AND4: Y4 and D4 → Output O4 AND5: Y5 and D5 → Output O5 AND6: Y6 and D6 → Output O6 AND7: Y7 and D7 → Output O7

8-input OR Gate

The output of all AND gates is connected to the 8-input OR gate. The final output Y_MUX is calculated as:

Y_MUX O0 ∨ O1 ∨ O2 ∨ O3 ∨ O4 ∨ O5 ∨ O6 ∨ O7

Logic Diagram

A simplified logic diagram representing the configuration is as follows:

Figure 1: Logic Diagram of 8-to-1 MUX with Decoder and Gates S2 --- 3-to-8 Decoder --- Y0 ----- AND0 -- S1 --- --- Y1 ----- AND1 -- S0 --- --- Y2 ----- AND2 -- --- Y3 ----- AND3 -- --- Y4 ----- AND4 -- --- Y5 ----- AND5 -- --- Y6 ----- AND6 -- --- Y7 ----- AND7 --

D0 ---------------------------------------

D1 ---------------------------------------

D2 ---------------------------------------

D3 ---------------------------------------

D4 ---------------------------------------

D5 ---------------------------------------

D6 ---------------------------------------

D7 ---------------------------------------

--- 8-input OR --- Y_MUX

Operation

When the select lines S2 S1 S0 are set to a specific value, the corresponding output Y_i from the decoder becomes HIGH. This signal enables the respective AND gate, which combines with the corresponding data input D_i. The OR gate then combines these outputs, producing the final output Y_MUX equal to the selected data input D_i.

Conclusion

This configuration efficiently implements an 8-to-1 multiplexer using a 3-to-8 line decoder and AND/OR gates, providing a clear and practical implementation method for multiplexing in digital circuits.