XOR/XNOR gate using 2:1 MUX

2-input XOR gate using a 2:1 multiplexer: As we know, a 2:1 multiplexer selects between two inputs depending upon the value of its select input. The function of a 2:1 multiplexer can be given as:

OUT = IN0 when SEL = 0 ELSE IN1

Also, a 2-input XOR gate produces a ‘1’ at the output if both the inputs have different value; and ‘0’ if the inputs are same. The truth table of an XOR gate is given as:

A	B	OUT
0	0	0
0	1	1
1	0	1
1	1	0

Truth table of XOR gate

In the truth table of XOR gate, if we fix a value, say B, then

OUT = A WHEN B = 0 ELSE A’

Both the above equations seem equivalent if we connect negative of IN0 to IN1 in a multiplexer. This is how a 2:1 multiplexer will implement an XOR gate. Figure 1 below shows the implement of a 2-input XOR gate using a 2:1 Multiplexer.

Implementing a 2-input XOR gate using a 2:1 Multiplexer

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2-input XNOR gate using a 2:1 multiplexer: Similarly, the truth table of XNOR gate can be written as:

A	B	OUT
0	0	1
0	1	0
1	0	0
1	1	1

Truth table of XNOR gate

In the truth table, if we fix, say A, then

OUT = B WHEN A = 1, ELSE B’

Thus, XNOR gate is the complement of XOR gate. It can be implemented if we connect A to IN1 and Abar to IN0.

2-input XNOR gate using 2:1 multiplexer

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