2-to-1 Multiplexer and a NOT gate to create XOR

Question

How do I implement the 2-input XOR logic function using only a 2-to-1 multiplexer and a NOT gate? 

Thanks. 

Answer 1

 

The 2-to-1 multiplexer is not necessary, complicates things, and is a WASTE.

Doubling the A as input into the multiplexer will satisfy this pesky

requirement. That is, input A into both inputs of the multiplexer so that A is the output

regardless of the selector. 

 

 

You will need an AND gate followed by the NOT gate in one branch.

The second branch shall be an OR gate

 

then send the output of these into another AND gate and the problem is solved.

 

You may need 2 TEEs or duplicators

 

The expression is:

 

 NOT (A and B)  and ( A or B)

 

Here's the truth table, which shows this expression is logically equivalent to the XOR

 

A     b       A and B            not (A and B)           A or B            FINAL AND    XOR
0     0              0                        1                       0                      0            0
0     1              0                        1                       1                      1            1
1     0              0                        1                       1                      1            1
1     1              1                        0                       1                      0            0

 

 

I have uploaded the circuit diagram for you in the RESOURCES section. The file name is XOR CIRCUIT.jpeg