2-1 multiplexer using only nands and nots

[mathrocks]

I need to make a 2-1 mux using only NANDS and inverters. I thought it would look like a simple nand gate with another inverter attached at the end (basically a AND gate). However, that didnt work. I need it so when the selection input is a zero it selects whatever X0 is and when the selection input is a 1 it will always select 0. I know how implement it using 3 NAND gates and an inverter. But I thought since one input is constantly grounded, there would be a a lot simplifed version.

Thanks

 

[dduardo]

When you try and figure out these problems it is always best to write out the truth table and solve the 3 variable k-map (for this case).

Hint: If the output of the MUX is X0 when S = 0 and the output of the MUX is 0 when S=1, then you'll need 2 inverters and 1 NAND.

 

[ravenprp]

for your question! Yes, you are correct that a 2-1 multiplexer can be simplified using only NAND gates and inverters. Here is a possible solution:

First, let's label our inputs as X0 and X1, and our selection input as S. Our output will be labeled as Y.

To begin, we can use a NAND gate with X0 and S as inputs, and the output of this gate will be one of our inputs for our final NAND gate. This first NAND gate will have the following truth table:

X0 | S | Output
0 | 0 | 1
1 | 0 | 1
0 | 1 | 0
1 | 1 | 0

Next, we can use another NAND gate with X1 and the output of the first NAND gate as inputs. This will be our second input for our final NAND gate. This second NAND gate will have the following truth table:

X1 | Output of first NAND gate | Output
0 | 1 | 1
1 | 1 | 0
0 | 0 | 1
1 | 0 | 0

Finally, we can use a NAND gate with the output of the second NAND gate and the selection input S as inputs. This will give us our final output Y. The truth table for this final NAND gate will be:

Output of second NAND gate | S | Output Y
1 | 0 | 1
0 | 1 | 0

As you can see, this simplified version only uses two NAND gates and one inverter, as opposed to the three NAND gates and inverter in the traditional 2-1 multiplexer. I hope this helps and let me know if you have any further questions!