Solving multiplexer circuit

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)