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GATE CSE 2024 Session 2 Q50: Output of AND, OR and XOR of four minterm functions

Question

Consider 4-variable functions f1, f2, f3, f4 expressed in sum-of-minterms form as given below.

f1=∑(0,2,3,5,7,8,11,13)f2=∑(1,3,5,7,11,13,15)f3=∑(0,1,4,11)f4=∑(0,2,6,13)\begin{aligned} f1 &= \textstyle\sum(0,2,3,5,7,8,11,13) \\ f2 &= \textstyle\sum(1,3,5,7,11,13,15) \\ f3 &= \textstyle\sum(0,1,4,11) \\ f4 &= \textstyle\sum(0,2,6,13) \end{aligned}

Circuit: f1 and f2 feed an AND gate, f3 and f4 feed an OR gate, and the two gate outputs feed an XOR gate whose output is Y
Tap the figure to enlarge

With respect to the circuit given above, which of the following options is/are CORRECT?

Try it: multiple select: one or more correct options

Select one or more options
Select all correct options. No negative marking, no partial marks.
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Answer: C, D (official GATE 2024 final answer key)

Concept used: On minterm sets, AND is intersection, OR is union and XOR is symmetric difference.

First step: f1·f2 = {3,5,7,11,13}\{3,5,7,11,13\} and f3 + f4 = {0,1,2,4,6,11,13}\{0,1,2,4,6,11,13\}; take the minterms in exactly one of them.

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Source: official GATE 2024 Session 2 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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