If the Output of two NAND gates is given to input of a NAND gate. Then the truth table will be of

Options

A. NOR gate
B. OR gate
C. AND gate
D. XOR gate

Answer

To solve the problem of determining the truth table when the output of two NAND gates is given to the input of another NAND gate, we can follow these steps:

### Step 1: Understand the NAND Gate
A NAND gate outputs a low signal (0) only when all its inputs are high (1). The output is high (1) in all other cases. The truth table for a single NAND gate with inputs A and B is as follows:

| A | B | Output (A NAND B) |
|---|---|-------------------|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |

### Step 2: Set Up the Inputs for Two NAND Gates
Let's denote the inputs to the first two NAND gates as A and B. The outputs of these two gates will be the inputs to the third NAND gate.

- **Output of NAND Gate 1 (O1)**: This will be the output of the first NAND gate with inputs A and B.
- **Output of NAND Gate 2 (O2)**: This will also be the output of the second NAND gate with the same inputs A and B.

### Step 3: Calculate Outputs of the First Two NAND Gates
Using the truth table of the NAND gate, we can find the outputs O1 and O2 for all combinations of A and B:

| A | B | O1 (A NAND B) | O2 (A NAND B) |
|---|---|----------------|----------------|
| 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |

### Step 4: Determine the Inputs for the Third NAND Gate
The outputs O1 and O2 from the first two NAND gates will serve as the inputs to the third NAND gate. The inputs to the third NAND gate will be:

- Input 1: O1
- Input 2: O2

### Step 5: Calculate the Output of the Third NAND Gate
Now, we will calculate the output of the third NAND gate based on the outputs O1 and O2:

| O1 | O2 | Output (O1 NAND O2) |
|----|----|----------------------|
| 1 | 1 | 0 |
| 1 | 1 | 0 |
| 1 | 1 | 0 |
| 0 | 0 | 1 |

### Step 6: Final Truth Table
Now, we can compile the final truth table that includes inputs A, B, and the output of the third NAND gate:

| A | B | Output (Final) |
|---|---|----------------|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |

### Conclusion
The output of the third NAND gate, which takes the outputs of two NAND gates as inputs, behaves like an AND gate. Therefore, the final output can be summarized as:

- The output is 1 when both inputs A and B are not both 1.
- The output is 0 when both inputs A and B are 1.