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# Solving multiplexer circuit

• Last Updated : 14 May, 2020

The procedure for solving and finding the output function of the given multiplexer is quite simple. Firstly we will discuss the procedure and then illustrate it with examples.

Procedure:

• Firstly truth table is constructed for the given multiplexer.
• Select lines in multiplexer are considered as input for the truth table.
• Output in truth table can be four forms i.e. ( 0, 1, Q, Q’).
• Now with the help of truth table we find the extended expression.
• Then the expression is minimized using boolean algebraic rules.
• Final function can be either in expression form or in SOP or POS form.

Example-1:
Given MUX is following, Explanation :

• Step-1: First draw the truth table. For the truth table, select lines A and B are the input.
According to the circuit,
```I0 = C' (hence first row of truth table will be C')
I1 = C'
I2 = C
I3 = C ```

I0, I1, I2, I3 are considered as output of 1st, 2nd, 3rd and 4th row of truth table respectively. • Step-2: Now we will find the expression of Y:
```Y = A'B'C' + A'BC' + AB'C + ABC
= A'C'(B' + B) + AC(B' + B)
= A'C' + AC
```

Example-2:
Given MUX, Explanation :

• Step-1: Truth table is following. For the truth table select lines B and C are input.
According to the circuit,
```I0 = A (hence first row of truth table will be A)
I1 = A'
I2 = 1
I3 = 0 ```

I0, I1, I2, I3 are considered as output of 1st, 2nd, 3rd and 4th row of truth table respectively. • Step-2: Now we will find the output:
```f(A, B, C) = AB'C' + A'B'C + BC'.1
= AB'C' + A'B'C + BC'(A + A')
= AB'C' + A'B'C + ABC' + A'BC'
=  100     001    110     010
= m(1, 2, 4, 6)```

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