How many minimum numbers of two input NAND gates are required to implement…
How many minimum numbers of two input NAND gates are required to implement boolean function f= p’qrs?
Answer: 7 — To implement the Boolean function f = p'qrs using two-input NAND gates, we need to break down the expression into basic logic operations that can be realized…
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Correct answer: 7
To implement the Boolean function f = p'qrs using two-input NAND gates, we need to break down the expression into basic logic operations that can be realized with NAND gates.
Step 1: Generate p' (NOT p). This requires one NAND gate configured as an inverter (both inputs connected to p).
Step 2: Generate qrs. This is an AND of three variables. We can implement this using NAND gates by first computing q AND r, then combining the result with s.
Step 3: Compute qr using a NAND gate followed by an inverter (another NAND gate used as inverter). This takes 2 gates.
Step 4: Compute (qr) AND s. Use a NAND gate on (qr) and s, then invert the output using another NAND gate as inverter. This takes 2 gates.
Step 5: Compute p' AND (qrs). Use a NAND gate on p' and (qrs), then invert the output using a NAND gate as inverter. This takes 2 gates.
Total gate count: 1 (for p') + 2 (for qr) + 2 (for qrs) + 2 (for final AND) = 7 gates.
Note: Each AND operation requires two NAND gates (one NAND followed by an inverter), and each NOT operation requires one NAND gate configured as an inverter.