The logic circuit shown below is equivalent to

Question

The logic circuit shown below is equivalent to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Output of first OR gate is A = (X+ barY) Inputs of second OR gate are barX and barA. Output of second OR gate is C = barX + barA = barX + overlineX+ barY = barX +( barX⋅ bar barY) = barX +( barX⋅ Y) = barX(1+Y) = barX Final output is z = barC = bar barX = X

Q. The logic circuit shown below is equivalent to

Output of first OR gate is A=(X+Yˉ) Inputs of second OR gate are Xˉ and Aˉ. Output of second OR gate is C=Xˉ+Aˉ =Xˉ+X+Yˉ​=Xˉ+(Xˉ⋅Yˉˉ)=Xˉ+(Xˉ⋅Y) =Xˉ(1+Y)=Xˉ Final output is z=Cˉ=Xˉˉ=X