Question

The combination of the gates shown below produces where $G_1$ to $G_4$ are NOR gates:

• A. AND gate
• B. XOR gate
• C. NOR gate
• D. NAND gate

Answer 1

The correct option is A AND gate

Observe that the input terminals for $G_1,G_2$ and $G_4$ are same.

Thus, the $\text{NOR}$ gate acts as a $\text{NOT}$ gate.

Let $A^{\prime }$ and $B^{\prime }$ be the complements of $A$ and $B$ respectively.

Replacing $G_1,G_2,G_4$ by $\text{NOT}$ gates, the logic statement of the given circuit is

$\text{NOT}\left(\text{OR}\right(\text{NOT}\left(A\right),\text{NOT}\left(B\right)\left)\right)\sim \text{NOT}\left(\text{OR}\right(A^{\prime },B^{\prime }\left)\right)\sim \text{NOT}(A^{\prime }\cup B^{\prime })\sim (A^{\prime }{)}^{\prime }\cap (B^{\prime }{)}^{\prime }=A\cap B=\text{AND}(A,B)$

Thus, the system behaves as an $\text{AND}$ gate.