Question

How many NAND gates are used to form AND gate? (A) 1 (B) 2 (C) 3 (D) 4

Short answer

Three NAND gates are used to form an AND gate.

Step-by-step solution

Recall the Truth Table for AND and NAND Gates

First, let's recall the truth table for AND and NAND gates: AND Gate: Input A | Input B | Output (A AND B) 0 | 0 | 0 0 | 1 | 0 1 | 0 | 0 1 | 1 | 1 NAND Gate: Input A | Input B | Output (A NAND B) 0 | 0 | 1 0 | 1 | 1 1 | 0 | 1 1 | 1 | 0 The objective is to use multiple NAND gates in such a way that the overall output is equivalent to an AND gate.

Creating the AND gate using NAND gates

Suppose we have three NAND gates. Let's label them NAND1, NAND2, and NAND3. We will connect these gates in the following manner: - Connect the inputs A and B to the inputs of NAND1. - Connect the output of NAND1 to both inputs of NAND2. - Connect the output of NAND2 to both inputs of NAND3. Now, let's analyze the output of each NAND gate based on the inputs A and B: 1. If A = 0, B = 0: - Output of NAND1 = 1; since NAND1 input is (0,0) - Output of NAND2 = 0; since NAND2 input is (1,1) - Output of NAND3 = 1; since NAND3 input is (0,0) - Overall Output = 0; which is equivalent to AND gate output for input (0,0) 2. If A = 0, B = 1: - Output of NAND1 = 1; since NAND1 input is (0,1) - Output of NAND2 = 0; since NAND2 input is (1,1) - Output of NAND3 = 1; since NAND3 input is (0,0) - Overall Output = 0; which is equivalent to AND gate output for input (0,1) 3. If A = 1, B = 0: - Output of NAND1 = 1; since NAND1 input is (1,0) - Output of NAND2 = 0; since NAND2 input is (1,1) - Output of NAND3 = 1; since NAND3 input is (0,0) - Overall Output = 0; which is equivalent to AND gate output for input (1,0) 4. If A = 1, B = 1: - Output of NAND1 = 0; since NAND1 input is (1,1) - Output of NAND2 = 1; since NAND2 input is (0,0) - Output of NAND3 = 1; since NAND3 input is (1,1) - Overall Output = 1; which is equivalent to AND gate output for input (1,1) As you can see, by connecting three NAND gates in the manner mentioned above, we have created an AND gate. Therefore, the correct answer is: (C) 3