Consider the following logic circuit whose inputs are functions and whose…

2002

Consider the following logic circuit whose inputs are functions and whose output is f.

logic circuit with inputs f1, f2, f3 and output f

Figure label note: the three input functions from top to bottom are f1(x, y, z), f2(x, y, z), and f3(x, y, z), respectively.

Given that

f1(x, y, z) = ∑(0, 1, 3, 5),
f2(x, y, z) = ∑(6, 7) and
f(x, y, z) = ∑(1, 4, 5),

f3 is:

Answer: A. ∑(1, 4, 5) — From the circuit, the first NAND gate gives (f1 f2)' and the lower inverter gives f3'. These two signals enter the final NAND gate, so f = [(f1 f2)' · f3']' =…

  1. A.

    ∑(1, 4, 5)

  2. B.

    ∑(6, 7)

  3. C.

    ∑(0, 1, 3, 5)

  4. D.

    None of these

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Correct answer: A

From the circuit, the first NAND gate gives (f1 f2)' and the lower inverter gives f3'. These two signals enter the final NAND gate, so f = [(f1 f2)' · f3']' = f1 f2 + f3 by De Morgan's law. Now f1 = Σ(0, 1, 3, 5) and f2 = Σ(6, 7). Their minterm sets have no intersection, so f1 f2 = 0. Hence f = f3. Since the given output is f = Σ(1, 4, 5), we get f3 = Σ(1, 4, 5).

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