Identify the logic operation carried out by the given circuit:

We need to determine the equivalent logic operation carried out by the given digital circuit arrangement.

1. Identify the Component Logic Gates

From the schematic layout, the circuit consists of three logic gates connected in series:

• Input Gates: Two single-input NAND gates acting as NOT gates for inputs $$A$$ and $$B$$.
• Output Gate: One two-input AND gate that combines the intermediate signals to produce output $$Z$$.

2. Analyze Intermediate Outputs ($$X$$ and $$Y$$)

When both input terminals of a NAND gate are shorted together, it functions strictly as an inverter (NOT gate):

• Upper Channel:
  Input $$A$$ passes through the shorted NAND gate, giving intermediate output $$X$$:

  $$X = \bar{A}$$

• Lower Channel:
  Input $$B$$ passes through the shorted NAND gate, giving intermediate output $$Y$$:

  $$Y = \bar{B}$$

3. Determine the Final Output Expression ($$Z$$)

The signals $$X$$ and $$Y$$ serve as inputs to the final AND gate. The Boolean expression for the final output $$Z$$ is calculated as follows:

$$Z = X \cdot Y$$

Substituting the values of $$X$$ and $$Y$$ into the equation gives:

$$Z = \bar{A} \cdot \bar{B}$$

Applying De Morgan's Law ($$\bar{A} \cdot \bar{B} = \overline{A + B}$$), we can simplify the expression:

$$Z = \overline{A + B}$$

4. Construct the Truth Table Verification

We can verify this Boolean expression by analyzing the state combinations of the truth table:

The output truth value matches the standard operational behavior of a NOR logic gate, where the output is high ($1$) only when all inputs are low ($0$).

Conclusion

The logic operation carried out by the given circuit configuration is a NOR gate.