The number of two input NAND gate required to implement an OR gate and...
OR gate using NAND gate:
EX-NOR gate using NAND gate:
Thus, we require 3 NAND gates for an OR gate while 5 NAND gates for an EX-NOR gate.
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The number of two input NAND gate required to implement an OR gate and...
Explanation:
To implement an OR gate using NAND gates, we need to consider the truth table of an OR gate, which is as follows:
| A | B | Output |
|---|---|--------|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
From the truth table, we can see that the output of an OR gate is 0 only when both inputs are 0. In all other cases, the output is 1.
To implement this behavior using NAND gates, we can connect two NAND gates in series, with their inputs connected to the same signal. The output of the first NAND gate will be connected to both inputs of the second NAND gate. The resulting circuit will function as an OR gate.
Implementation of OR gate using NAND gates:
- Input A and B are connected to the inputs of two NAND gates.
- The outputs of both NAND gates are connected to the inputs of a third NAND gate.
- The output of the third NAND gate is the output of the OR gate.
Truth table for the implementation:
| A | B | NAND1 | NAND2 | Output |
|---|---|-------|-------|--------|
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 |
As we can see from the truth table, the implementation using three NAND gates behaves exactly like an OR gate.
Implementation of EX-NOR gate using NAND gates:
To implement an EX-NOR gate using NAND gates, we can use the following logic:
EX-NOR(A, B) = NAND(NAND(A, NAND(A, B)), NAND(B, NAND(A, B)))
- First, we NAND the inputs A and B together.
- Then, we NAND the result with A and B separately.
- Finally, we NAND the results of the previous step together.
Implementation of EX-NOR gate using NAND gates:
- Input A and B are connected to the inputs of a NAND gate.
- The output of the NAND gate is connected to one input of two separate NAND gates.
- Input A is connected to the other input of the first NAND gate.
- Input B is connected to the other input of the second NAND gate.
- The outputs of both NAND gates are connected to the inputs of a third NAND gate.
- The output of the third NAND gate is the output of the EX-NOR gate.
Truth table for the implementation:
| A | B | NAND1 | NAND2 | NAND3 | Output |
|---|---|-------|-------|-------|--------|
| 0 | 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 0
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