The logic operations performed by the given digital circuit is equivalent to:
- NAND
- NOR
- OR
- AND
The Correct Option is D
Solution and Explanation
Step 1: Analyze the First NAND Gate
The output of the first (topmost) NAND gate is:
\[ \overline{A \cdot B}. \]
This output is also connected as an input to the second NAND gate (middle). Let this output be \( X_1 \):
\[ X_1 = \overline{A \cdot B}. \]
Step 2: Analyze the Second NAND Gate
The second NAND gate takes \( X_1 \) and the output of the third NAND gate (\( X_2 \)) as inputs. The output of the second NAND gate is:
\[ X_3 = \overline{X_1 \cdot X_2}. \]
From the first NAND gate, \( X_1 = \overline{A \cdot B} \), and from the third NAND gate, \( X_2 = \overline{A \cdot B} \). Substituting these values:
\[ X_3 = \overline{\overline{A \cdot B} \cdot \overline{A \cdot B}}. \]
Using the property of NAND gates:
\[ X_3 = A \cdot B. \]
Step 3: Analyze the NOT Gate
The NOT gate inverts the output of the second NAND gate. Let \( Y \) be the output of the NOT gate. Then:
\[ Y = \overline{X_3}. \]
Substituting \( X_3 = A \cdot B \):
\[ Y = A \cdot B. \]
Step 4: Simplify the Expression
Using Boolean algebra, the final output \( Y \) simplifies to:
\[ Y = A \cdot B. \]
This represents the logic for an AND gate.
Final Answer:
The given digital circuit is equivalent to an AND gate.
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Concepts Used:
Logic Gates
AND Gate
It is the gate, where a circuit performs an AND operation. It has n number of input where (n >= 2) and one output.
OR Gate
It is the gate, where a circuit performs an OR operation. It has n number of input where (n >= 2) and one output.
NOT Gate
An inverter is also called NOT Gate. It has one input and one output where the input is A and the output is Y.
NAND Gate
A NAND operation is also called a NOT-AND operation. It has n number of input where (n >= 2) and one output.
NOR Gate
A NOR operation is also called a NOT-OR operation. It has n number of input where (n >= 2) and one output.
XOR Gate
XOR or Ex-OR gate is a specific type of gate that can be used in the half adder, full adder, and subtractor.
XNOR Gate
XNOR gate is a specific type of gate, which can be used in the half adder, full adder, and subtractor. The exclusive-NOR gate is flattened as an EX-NOR gate or sometimes as an X-NOR gate. It has n number of input (n >= 2) and one output.