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Solving multiplexer circuit

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  • Difficulty Level : Medium
  • Last Updated : 14 May, 2020
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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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