OR gate can be represented with __________ NAND gatesQuestion 3Answera.threeb.twoc.fourd.one

To determine how many NAND gates are needed to construct an OR gate, we can follow these steps:

1. Break Down the Problem

We need to express an OR gate in terms of NAND gates. An OR gate can be created using the properties of NAND gates.

2. Relevant Concepts

We will use the fact that:

• The OR function can be expressed using NAND with De Morgan's theorem.
• The equation for an OR gate can be represented as: $A \lor B = \neg(\neg A \land \neg B)$ Using NAND gates, this can be translated as:
• First compute $\neg A$ and $\neg B$ using NAND: $\neg A = A \text{ NAND } A$ $\neg B = B \text{ NAND } B$
• Then compute $\neg(\neg A \land \neg B)$ as: $A \lor B = (\neg A \text{ NAND } \neg B) = (A \text{ NAND } A) \text{ NAND } (B \text{ NAND } B)$

3. Analysis and Detail

Let's calculate:

• To find the OR of two inputs $A$ and $B$ using NAND gates, we need:
  • 2 NAND gates to generate $\neg A$ and $\neg B$.
  • 1 NAND gate to combine $\neg A$ and $\neg B$ to get the final output.

Thus, we have a total of:

• 2 (for $\neg A$ and $\neg B$) + 1 (for combining) = 3 NAND gates.

4. Verify and Summarize

We've effectively broken down the construction of an OR gate using NAND gates:

1. $\neg A$ using 1 NAND,
2. $\neg B$ using another NAND,
3. Combine $\neg A$ and $\neg B$ using one more NAND.

Final Answer

The correct answer is three.