Consider the Boolean function \(z(a,b,c)\). Which one of the following minterm…
2020
Consider the Boolean function \(z(a,b,c)\).
Which one of the following minterm lists represents the circuit given above ?
- A.
\(z=\sum (0,1,3,7)\) - B.
\(z=\sum (1,4,5,6,7)\) - C.
\(z=\sum (2,4,5,6,7)\) - D.
\(z=\sum (2,3,5)\)
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Correct answer: B
Final expression: z = a + (not b AND c)
Reasoning: The circuit shows an OR gate whose inputs are a and the output of an AND gate. The AND gate takes the inverted b and c as inputs, so its output is (not b AND c). Therefore the overall function is z = a + (not b AND c).
When a = 1 the output z is 1 for all values of b and c, giving minterms 4, 5, 6, 7.
When a = 0 the output depends on (not b AND c), which is 1 only when b = 0 and c = 1, corresponding to minterm 1.
Combine both cases to get the full minterm list: 1, 4, 5, 6, 7.
Final minterm representation: z = Σ(1, 4, 5, 6, 7)