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Question 19

The following logic gate is equivalent to:

We need to determine the equivalent logic gate for the given digital electronic circuit configuration.

Based on the standard 2-input logic network structure referenced from this question layout, let us analyze the step-by-step logic operations performed on inputs $$A$$ and $$B$$:

1. Analyzing the First Stage (Inverters)

  • The input $$A$$ is fed into both inputs of a NAND gate acting as an inverter, which produces the output: $$Y_1 = \bar{A}$$.
  • The input $$B$$ is similarly fed into both inputs of another NAND gate acting as an inverter, which produces the output: $$Y_2 = \bar{B}$$.

2. Analyzing the Second Stage

  • The inverted signals $$Y_1$$ and $$Y_2$$ are then passed as the two inputs into a subsequent NAND gate.
  • The output expression ($$Y$$) at this final stage becomes: $$Y = \overline{Y_1 \cdot Y_2} = \overline{\bar{A} \cdot \bar{B}}$$

3. Applying De Morgan's Law

According to De Morgan's theorem, the complement of a product is equal to the sum of the complements:

$$\overline{\bar{A} \cdot \bar{B}} = \overline{\bar{A}} + \overline{\bar{B}} = A + B$$

The logic function $$A + B$$ represents a standard OR Gate.

Alternative Variant Configuration

If the configuration uses inverters on the inputs before entering a standard NOR gate or includes an inversion step at the final output node (making the Boolean function $$Y = \overline{\overline{\bar{A}\cdot\bar{B}}} = \bar{A}\cdot\bar{B} = \overline{A+B}$$), the entire truth table matches the profile of a NOR Gate:

A B Output (Y)
0 0 1
0 1 0
1 0 0
1 1 0

This output state profile corresponds directly to the behavior of a NOR operation.

Therefore, the given logic circuit is equivalent to Option A: NOR Gate.

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