Question 9147 – GATE 2008

Given f1, f3 and f in canonical sum of products form (in decimal) for the circuit

    f1 = Σm(4,5,6,7,8)
    f3 = Σm(1,6,15)
    f = Σm(1,6,8,15)

then f2 is

Correct Answer: C

Question 8 Explanation: 
f = f1* f2 + f3
f1*f2 is intersection of minterms of f1 and f2
f = (f1*f2) + f3 is union of minterms of (f1*f2) and f3
Σm(1,6,8,15) = Σm(4,5,6,7,8) * f2 + Σm(1,6,15)
Options A, B and D have minterm m4 which result in Σm(1,4,6,15), Σm(1,4,6,8, 15) and Σm(1,4,6,8, 15)respectively and they are not equal to f.
Option C : If f2 = Σm(6,8)

RHS: Σm(4,5,6,7,8) * Σm(6,8) + Σm(1,6,15)
= Σm(6,8) + Σm(1,6,15)
= Σm(1,6,8,15)
= f = LHS
A
Σm(4,6)
B
Σm(4,8)
C
Σm(6,8)
D
Σm(4,6,8)
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