To determine which of the following gates is reversible, we need to analyze each gate and see if the output can uniquely determine the input. A gate is considered reversible if the output can be used to retrieve the original input without any loss of information.
### Step-by-Step Solution:
1. **Understanding Reversibility**: A gate is reversible if for every possible output, there is a unique input that produces it. This means that the output must be able to provide enough information to recover the input.
2. **Analyzing the First Gate (NOT Gate)**:
- The NOT gate takes a single input A and produces an output that is the logical negation of A.
- If the input A is 0, the output is 1; if the input A is 1, the output is 0.
- In this case, we cannot uniquely determine the input from the output because knowing the output does not allow us to recover the original input. Thus, the NOT gate is not reversible.
3. **Analyzing the Second Gate (NAND Gate)**:
- The NAND gate takes two inputs A and B and produces an output that is the negation of the AND operation on A and B, i.e., output = ¬(A · B).
- For example, if A = 0 and B = 0, the output is 1; if A = 1 and B = 1, the output is 0.
- Similar to the NOT gate, the output does not uniquely determine the inputs A and B. Therefore, the NAND gate is not reversible.
4. **Analyzing the Third Gate (OR Gate)**:
- The OR gate takes two inputs A and B and produces an output that is the logical disjunction of A and B, i.e., output = A + B.
- For example, if A = 0 and B = 1, the output is 1. However, if A = 1 and B = 0, the output is also 1.
- Again, the output does not uniquely determine the inputs, making the OR gate not reversible.
5. **Analyzing the Fourth Gate (AND Gate)**:
- The AND gate takes two inputs A and B and produces an output that is the logical conjunction of A and B, i.e., output = A · B.
- Similar to the previous gates, the output does not uniquely determine the inputs A and B. Thus, the AND gate is also not reversible.
6. **Conclusion**: After analyzing all the gates, we find that none of the gates mentioned (NOT, NAND, OR, AND) are reversible. Therefore, the answer to the question is that none of the gates listed is reversible.
