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The image you uploaded describes a 4-bit circuit capable of adding or subtracting binary numbers, which are in two's complement form (negative numbers are represented in complement form). This circuit likely represents a 4-bit adder/subtractor using XOR gates and full adders.

### Problem Breakdown:
- **Add/Subtract Input:** This controls whether the circuit adds or subtracts two binary numbers. This is a common feature in many computer arithmetic logic units (ALUs).
- **4-Bit Binary Numbers (A and B):** The inputs are four bits wide (A3 A2 A1 A0 for one number and B3 B2 B1 B0 for the other number).

### Explanation:
#### Part (a): When the Add/Subtract Input is HIGH
When the Add/Subtract input is high, the circuit performs a subtraction operation. Here’s what happens in more detail:
1. **Subtraction in Binary**: To subtract a number in binary, the circuit adds the two's complement of the second number. This is achieved by inverting each bit of the second number (B3 B2 B1 B0) and adding 1 to the least significant bit (LSB).
2. **Inversion using XOR Gate**: The XOR gates shown in the diagram are used to invert each bit of the second input (B3 B2 B1 B0) when the Add/Subtract signal is high (logic 1). If Add/Subtract is high, each XOR gate will flip the corresponding bit of B (i.e., B becomes ¬B).
3. **Adding 1 (Two's Complement Step)**: The carry-in for the least significant bit (C_in0) is set to 1 when the circuit is in subtract mode, representing the addition of 1 needed for two's complement.

#### Part (b): When the Add/Subtract Input is LOW
When the Add/Subtract input is low, the circuit performs an addition operation:
1. **Binary Addition**: In this case, the XOR gates do not invert the second input (B3 B2 B1 B0) because Add/Subtract is 0. Thus, the inputs are passed unchanged into the adders.
2. **Carry-in for Addition**: The carry-in for the least significant bit (C_in0) is set to 0 because no two's complement is needed.

### Summary:
- **Add/Subtract HIGH (1)**: The circuit subtracts B from A by inverting the B inputs and adding 1 (two's complement).
- **Add/Subtract LOW (0)**: The circuit performs a straightforward addition of A and B.

Let me know if you need any more details or further clarification!

### Relative Questions:
1. What is the role of XOR gates in a binary adder/subtractor circuit?
2. How does the carry-in affect the result when performing subtraction?
3. How does two's complement representation simplify binary subtraction?
4. What would happen if the Add/Subtract input was not used in such circuits?
5. Can you explain the significance of overflow in binary addition and subtraction?

### Tip:
When performing binary subtraction using two's complement, always ensure the correct carry-in is applied to avoid errors in the final result.

Explain what happens in the 4-bit adder/subtractor circuit when the Add/Subtract input is HIGH or LOW.

Learn how a 4-bit adder/subtractor circuit operates using two's complement arithmetic. This explanation covers the role of the Add/Subtract input and XOR gates for binary addition and subtraction, suitable for college-level studies in digital logic and computer architecture.

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