GATE CS 2019 Set 1 — Question 40
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Digital Logic → Boolean Algebra & Logic Gates → Minterms & Maxterms
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Question
Consider three 4-variable functions , , and , which are expressed in sum-of-minterms as
, ,
For the following circuit with one AND gate and one XOR gate, the output function can be expressed as:
, ,
For the following circuit with one AND gate and one XOR gate, the output function can be expressed as:
Correct answer
(A) Σ (7, 8, 11)
Solution
From the circuit diagram:
Intersection (): Step 2: Calculate
Let and .
XOR operation corresponds to the symmetric difference: .
Thus, .
1.The AND gate takes inputs and . Its output is (intersection of minterms).
2.The XOR gate takes inputs and . Its output is .
Step 1: Calculate Intersection (): Step 2: Calculate
Let and .
XOR operation corresponds to the symmetric difference: .
Thus, .
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