Universal Logic : Mux to Logic gates conversion

We have seen the universal gates in out previous posts. The NAND and NOR are called the universal gates because they can create any of the logic gates.

There is an another concept called “Universal Logic”, Universal logic can also be used to create any of the logic gates.

MUX and Decoders are called “Universal Logic”

In this post, we will see haw a 2:1 MUX can be used to create different logic gates.

1. Designing an Inverter using 2:1 MUX.

To design an inverter using 2:1 mux, we have to use the input as the select line of the MUX and the “zeroth” select line would be tied with “Logic 1 ” and “First” select line would be tired with “Logic 0″, Now when the select line (Input) goes to “1″ the out put will be “0″ ( inverted).

Image : MUX to inverter -

2:1 mux as an inverter

2. Designing an AND Gate using 2:1 MUX.

To design an AND using 2:1 mux, we need to tie the “zeroth” input to “Logic 0″ and the “First” input to the one of the input of the AND Gate. The other input of AND gate would be connected with the select line of the MUX.

Now, the out put of the MUX would be “1″ only if the both of the inputs are “1″ otherwise it would be “0″ for all conditions.

Image : MUX to AND Gate -

2:1 MUX as an AND gate

3. Designing an OR Gate using 2:1 MUX.

To design an OR using 2:1 mux, we need to tie the “First” input to “Logic 1″ and the “Zeroth” input to the one of the input of the OR Gate. The other input of OR gate would be connected with the select line of the MUX.

Now, the output of the MUX would be “1″ when any oth the two inputs would be “1″ otherwise it would be “0″ for all conditions.

Image : MUX to OR Gate -

2:1 MUX as an OR Gate

4. Designing an NOR Gate using 2:1 MUX.

To design the NOR using 2:1 mux, we need to tie the “Zeroth” input of mux to one of the input of NOR and another input of MUX is tied to “0″ . The another input of NOR gate would be applied to the select line of the MUX.

Now, the output of the MUX would be A’B’ = (A+B)’. which is as same as the output of NOR Gate.

Image : MUX to NOR Gate -

2:1 mux as a NOR Gate

5. Designing an NAND Gate using 2:1 MUX.

To design the NAND using 2:1 mux, we need to combine the AND Gate and inverter implementation

6. Designing an XOR Gate using 2:1 MUX.

To design the XOR using 2:1 mux, we need to tie the “Zeroth” input of mux to one of the input of XOR and another input of MUX to the inverted of first input. The another input of XOR gate would be applied to the select line of the MUX.

Now, the output of the MUX would be AB’ + A’B which is as same as the output of XOR Gate.

Image : MUX to XOR Gate -

2:1 Mux as a XOR gate

7. Designing an XNOR Gate using 2:1 MUX.

To design the XNOR using 2:1 mux, we need to tie the “First” input of mux to one of the input of XOR and another input of MUX to the inverted of first input. The another input of XOR gate would be applied to the select line of the MUX.

Now, the output of the MUX would be A’B’ + AB which is as same as the output of XNOR Gate.

Image : MUX to XNOR Gate -

2:1 mux as a XNOR Gate

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