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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