In the digital circuit shown in the figure, for the given inputs the P and Q values are:
In the digital circuit shown in the figure, for the given inputs the P and Q values are:
Show Hint
- \( P = 1, Q = 1 \)
- \( P = 0, Q = 0 \)
- \( P = 0, Q = 1 \)
- \( P = 1, Q = 0 \)
The Correct Option is B
Approach Solution - 1
We are given a digital logic circuit where both inputs are logic 1 (HIGH). We need to determine the outputs \( P \) and \( Q \).
Concept Used:
Each logic gate performs a standard Boolean operation:
- AND gate: Output = 1 only if all inputs are 1.
- NAND gate: Output = NOT(AND) = 0 only if all inputs are 1.
- OR gate: Output = 1 if at least one input is 1.
- NOT gate (inverter): Output = complement of the input.
- NOR gate: Output = NOT(OR).
Step-by-Step Analysis:
Step 1: Identify inputs.
Both upper and lower inputs are given as logic 1 (HIGH).
Step 2: Top-left gate:
It is a NAND gate (AND gate with a bubble at output). Inputs = 1 and 1 → AND output = 1 → NAND output = NOT(1) = 0. \[ \text{Output of NAND gate} = 0 \]
Step 3: The output of this NAND gate (0) goes to two places:
- One input of the lower-left OR gate. - One input of the rightmost AND gate (for P).
Step 4: Bottom-left part:
The OR gate receives two inputs: - One is directly 1 (the lower input line). - The other is 0 (from the NAND gate). So OR output = 1.
Step 5: The OR gate output passes through a NOT gate:
NOT(1) = 0.
Step 6: This 0 goes into the NOR gate (the second circle with OR shape + bubble at output) along with the direct upper input (1).
NOR gate inputs: 1 and 0 → OR = 1 → NOR output = NOT(1) = 0. \[ Q = 0 \]
Step 7: Now find P:
The rightmost top AND gate receives: - One input = output of the first NAND = 0. - Another input = top input = 1. AND(1, 0) = 0. \[ P = 0 \]
Final Computation & Result
\[ P = 0,\quad Q = 0. \]
Correct Option: (2) \( P = 0, Q = 0 \)
Approach Solution -2
For the given digital circuit, follow the logic gates step by step.
Using the inputs \( P = 0 \) and \( Q = 1 \), we compute the outputs as follows:
- The AND gate gives \( 0 \)
- The NOT gate inverts the inputs appropriately.
Hence, the correct output for the given circuit is: \[ P = 0, Q = 0 \]
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