Three variable function can be easily implemented using 8:1 multiplexer.
connect 3 input lines to select lines of mux and connect 8 inputs of mux
to logic 0 or 1 according to function output. For example, let us say Function is
F(X,Y,Z) = Σ(0,1,3,6)
then
X,Y,Z will be connected to select lines of Mux and I0 , I1, I3 and I6
will be connected to logic 1(VDD) and other will be connected to logic 0
For
a 4 variable function, there are 16 possible combinations. To implement
4 variable function using 8:1 MUX, use 3 input as select lines of MUX
and remaining 4th input and function will determine ith input of mux .
Let us demonstrate it with an example :
A
|
B
|
C
|
D
|
Decimal
Equivalent
|
F
|
0
|
0
|
0
|
0
|
0
|
0
|
1
|
0
|
0
|
0
|
8
|
0
|
0
|
0
|
0
|
1
|
1
|
1
|
1
|
0
|
0
|
1
|
9
|
1
|
0
|
0
|
1
|
0
|
2
|
0
|
1
|
0
|
1
|
0
|
10
|
1
|
0
|
0
|
1
|
1
|
3
|
0
|
1
|
0
|
1
|
1
|
11
|
1
|
0
|
1
|
0
|
0
|
4
|
0
|
1
|
1
|
0
|
0
|
12
|
1
|
0
|
1
|
0
|
1
|
5
|
1
|
1
|
1
|
0
|
1
|
13
|
0
|
0
|
1
|
1
|
0
|
6
|
0
|
1
|
1
|
1
|
0
|
14
|
0
|
0
|
1
|
1
|
1
|
7
|
1
|
1
|
1
|
1
|
1
|
15
|
0
|
 |
| The 4 variable function represented using 8:1 mux |
ABar = ~A (inverted A)
for A = 0, F = 1
for A = 1, F = 0
Hence F = ~A (for BCD = 101)
I4, (B = 1, C = 0, D = 0), F = A
I1, (B = 0, C = 0,D = 1), F = 1 (irrespective of status of A)
similarly All other inputs can be inferred in the same way. Thus we can conclude that to implement n variable function, we need 2^(n-1) to 1 MUX and an inverter. n-1 input lines shall be used as select lines and rest one will be used for input of MUX.
Also read:
Also read: