Logic design using only NOR gates How many 2-input NOR gates are required to implement a 2-input NAND gate (using NOR gates only)?

Introduction / Context:
Universal gates such as NOR and NAND can be combined to realize any Boolean function. This question tests gate-level synthesis skills by asking how to build a 2-input NAND strictly from 2-input NOR gates, an essential technique when constrained to a single gate family.

Given Data / Assumptions:

• Available building block: 2-input NOR gates only.
• Target function: 2-input NAND, i.e., Y = (A * B)' = (A * B)' which equals (A * B)'.
• Allowed trick: use a NOR gate as an inverter by tying its inputs together (X NOR X = X').

Concept / Approach:
Apply DeMorgan's law to express NAND in terms of OR and complements: (A * B)' = A' + B'. If we can generate A' and B' with NOR inverters and then realize an OR using NOR, we can obtain NAND with only NOR devices.

Step-by-Step Solution:
1) Invert A with a NOR inverter: A1 = A NOR A = A'.2) Invert B with a NOR inverter: B1 = B NOR B = B'.3) Form the OR of A1 and B1 using NOR then invert: T = A1 NOR B1 = (A1 + B1)'.4) Invert T with a NOR inverter: Y = T NOR T = ((A1 + B1)')' = A1 + B1 = A' + B' = (A * B)' (the desired NAND).

Verification / Alternative check:
Truth-table check confirms that the composite four-NOR network outputs 0 only when A = B = 1, matching a NAND gate. A quick simulation or hand evaluation for all four input pairs verifies correctness.

Why Other Options Are Wrong:
1, 2, or 3 gates: Insufficient because you need at least two inverters (for A and B) plus a NOR-based OR (which itself requires a NOR and a final inversion).5 gates: Possible but not minimal; the construction above achieves the function with four NORs.

Common Pitfalls:
Forgetting that OR with NOR requires an additional inversion, or attempting to realize AND directly with NOR without proper inversions, which yields a different function (e.g., NOR rather than NAND).

Final Answer:
4