A boolean function f(X,Y,Z) is implemented using 3 x 8 decoder. Where X is MSB and Z is LSB in resulting output. The connection of fan-in is depicted below:

Then which of the following option is correct?
I – f(X,Y,Z) = Σ(0,3,6,7)
II – f(X,Y,Z) = π(0,2,4,7)
III – f(X,Y,Z) = Σ(0,3,5,7)
IV – f(X,Y,Z) = π(0,1,4,7)

(A) I and II
(B) I and IV
(C) II and III
(D) III and IV


Answer: (C)

Explanation: In the given decoder:

f(X,Y,Z) = I₀ + I₃ + I₆ + I₇
I₀ = X\’Z\’Y\’; Since, X is MSB and Z is LSB at output So, I₀ = X\’Y\’Z\’
Similarly,
I₃ = X\’ZY = X\’ZY = I₃
I₆ = XZY\’ = XY\’Z = I₅
I₇ = XZY = XYZ = I₇
f(X,Y,Z) = Σ(0,3,5,7) in SOP
f(X,Y,Z) = π(0,2,4,7) in POS
So, option (C) is correct.

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