Understanding Half Adder
A half adder is a fundamental digital circuit used in electronics to perform the arithmetic operation of addition on two binary digits. It has two inputs and two outputs.
Inputs and Outputs
- Inputs:
- A (first bit)
- B (second bit)
- Outputs:
- Sum (S)
- Carry (C)
Functionality
The half adder operates based on the following logic:
- Sum (S): The sum output is produced using the XOR (exclusive OR) operation. It gives a high output (1) when the inputs A and B are different (i.e., one is 1 and the other is 0).
- Carry (C): The carry output indicates whether there is an overflow from the addition of the two bits. It is generated using the AND operation and outputs a high signal (1) only when both inputs are 1.
Why is Half Adder Known as XOR?
- The half adder's primary function is to calculate the sum of two binary digits. The logic behind this is best represented by the XOR gate, which is defined by the following truth table:
| A | B | S (Sum) | C (Carry) |
|---|---|---------|-----------|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
- The output of the Sum (S) matches the behavior of the XOR gate, confirming that the half adder is also known as an XOR circuit.
Conclusion
In summary, the half adder is essential in digital circuits for binary addition, and its sum output is directly derived from the XOR operation, making option 'D' the correct answer.