In the adder circuits of two inputs

Options

A. AND gate is used for carry forward memory
B. XOR gate is used for display
C. Both (1) and (2)
D. none of these

Answer

To solve the question regarding the adder circuits of two inputs, we will analyze the half adder circuit, which consists of an AND gate and an XOR gate. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Understanding the Half Adder**:
- A half adder is a circuit that adds two single binary digits (bits) and produces a sum and a carry output.
- The two inputs are typically denoted as A and B.

2. **Identifying the Gates Used**:
- The half adder uses two types of logic gates:
- **XOR Gate**: This gate is used to calculate the sum (S) of the two inputs.
- **AND Gate**: This gate is used to calculate the carry (C) from the addition.

3. **Writing the Output Expressions**:
- The output of the XOR gate, which gives the sum (S), can be expressed as:
\[ S = A \oplus B = AB' + A'B \]
- The output of the AND gate, which gives the carry (C), can be expressed as:
\[ C = A \cdot B \]

4. **Conclusion**:
- In summary, for a half adder:
- The sum (S) is produced by the XOR gate.
- The carry (C) is produced by the AND gate.
- Therefore, both the expressions for sum and carry are valid.

5. **Selecting the Correct Options**:
- If the question provides multiple options regarding the outputs of the half adder, the correct options would include:
- The expression for the sum (S) and the expression for the carry (C).
- Hence, if options A and B correspond to these outputs, then both are correct.

### Final Answer:
Both options A and B are correct regarding the outputs of the half adder circuit.

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