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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