What is the minimum number of gates required to implement the Boolean function…
2009
What is the minimum number of gates required to implement the Boolean function (AB+C) if we have to use only 2-input NOR gates?
- A.
2
- B.
3
- C.
4
- D.
5
Attempted by 405 students.
Show answer & explanation
Correct answer: B
Answer: 3 gates.
Key identity used: AB + C = (A + C)(B + C).
Construction using 2-input NOR gates:
Gate 1: NOR(A, C) produces (A + C)'.
Gate 2: NOR(B, C) produces (B + C)'.
Gate 3: NOR(Gate1, Gate2) produces ((A + C)' + (B + C)')' which equals (A + C)(B + C) = AB + C.
Minimality argument:
The chosen construction computes two distinct complemented OR terms (A + C)' and (B + C)' as separate intermediate signals, then combines them with a NOR to produce the required AND of the uncomplemented ORs. Producing both intermediate terms requires at least two gates, and combining them requires a third gate.
With only two 2-input NOR gates you cannot generate both required intermediate complemented OR terms and then combine them, so two gates are insufficient.