A logic circuit combines an upper NOR gate and a lower NAND gate; their outputs feed a final AND gate (see figure). Which single logic gate has the same output? Image
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Question

A logic circuit combines an upper NOR gate and a lower NAND gate; their outputs feed a final AND gate (see figure). Which single logic gate has the same output? Image

G1 Physics · Accepted Answer

Step 1: The upper NOR gate produces X = (A + B)̅ (NOT of A OR B). Step 2: The lower NAND gate produces Z = (A·B)̅. Step 3: Final AND output is Y = X·Z = (A + B)̅ · (A·B)̅. Step 4: Whenever (A + B)̅ = 1, both inputs A and B equal 0, so (A·B)̅ = 1. Thus the second factor does not change X. Step 5: Y = (A + B)̅, exactly a NOR operation. Final answer: NOR gate, Option D.