Which one of the following circuits implements the Boolean function given below? f(x, y,z) = m0 + m1 + m3 +m4 + m5 + m6, where mi is the ith minterm.

Which one of the following circuits implements the Boolean function given below? f(x, y,z) = m0 + m1 + m3 +m4 + m5 + m6, where mi is the ith minterm. Correct Answer <img alt="F1 Raju.S 24-02-21 Savita D11" src="//storage.googleapis.com/tb-img/production/21/02/F1_Raju.S_24-02-21_Savita_D11.png" style="width: 177px; height: 156px;">

Answer: Option 1

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Concept : 

• Boolean expression  : S̅ ₁S̅ ₀I₀ + S̅ ₁ S₀I₁ + S₁S̅ ₀I₂ + S₁S₀I₃

Explanation :

Given :

F( x, y, z ) = m₀ + m₁ + m₃ + m₄ + m₅ + m₆

F( x, y, z ) = x’y’z’ + x’y’z + x’yz + xy’z’ + xy’z + xyz’

Now if we observe Given Question is a MCQ i.e. There will be only one Correct Option.

In given all options, Multiplexers have y, z as Select lines.

So we will try classify the input based on select line.(possible inputs) 

And other variables on input side.

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So Correct options is 1. 

Alternatively 

Alternatively,

Option 4 :

Boolean expression  : y’z’x’ + y’z(1) + yz’(x) + yz(1)

= x’y’z’ + xyz’ + y’z + yz

=  x’y’z’ + xyz’ + (x+x’)y’z + (x+x’)yz

= x’y’z’ + x’y’z + x’yz + xy’z + xyz’ + xyz

= m₀ + m₁ + m₃ + m₅ + m₆ + m₇

This is not equivalent to given expression in the Question.

Option 3 :

Boolean Expression :  y’z’(1) + y’z(1) + yz’(x’) + yz(x)

= x’yz’ + xyz + (x+x’)y’z’ + (x+x’)y’z

= x’y’z’ + x’y’z + x’yz’ + xy’z’ + xy’z + xyz

= m₀ + m₁ + m₂ + m₄ + m₅ + m₇  

Again, This is not equivalent to given expression in the Question.

Option 2 : 

Boolean Expression :  y’z’(x) + y’z(1) + yz’(x’) + yz(1)

= x’yz’ + xy’z’ + y’z + yz

= x’yz’ + xy’z’ + (x+x’)y’z + (x+x’)yz

= x’y’z + x’yz’ +x’yz + xy’z’ + xy’z + xyz

= m₁ + m₂ + m₃ + m₄ + m₅ + m₇

Again, This is not equivalent to given expression in the Question.

Option 1 : 

Boolean Expression : y’z’(1) + y’z(1) + yz’(x) + yz(x’)

= xyz’ + x’yz + y’z’ + y’z

= xyz’ + x’yz + (x+x’)y’z’ + (x+x’)y’z

= x’y’z’ + x’y’z + x’yz + xy’z’ +xy’z + xyz’

= m₀ + m₁ + m₃ + m₄ + m₅ + m₆

Hence this is the Correct Option.