Half Adder Gates

A half adder is a digital circuit that performs addition of two one-bit numbers. It has two inputs, A and B, and two outputs, Sum (S) and Carry (C). The Sum output represents the result of adding A and B, while the Carry output represents the carry that occurs when A and B are added.

To build a half adder, we need two basic logic gates: the EX-OR gate and the AND gate. The EX-OR gate produces a high output (1) when its two inputs are different, and a low output (0) when they are the same. The AND gate produces a high output (1) only when both of its inputs are high (1), and a low output (0) otherwise.

EX-OR Gate

The EX-OR gate (also known as the exclusive OR gate) is a two-input gate that produces a high output (1) when its two inputs are different, and a low output (0) when they are the same. The truth table for an EX-OR gate is shown below:

| Input A | Input B | Output |
|---------|---------|--------|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |

AND Gate

The AND gate is a two-input gate that produces a high output (1) only when both of its inputs are high (1), and a low output (0) otherwise. The truth table for an AND gate is shown below:

| Input A | Input B | Output |
|---------|---------|--------|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

Half Adder Circuit

The circuit diagram for a half adder using an EX-OR gate and an AND gate is shown below:

```
+-----+ +-----+
A----| |-----| |
| EX- | | AND |----S
B----| OR |-----| |
+-----+ +-----+
|
+----C
```

The EX-OR gate is used to calculate the Sum output, while the AND gate is used to calculate the Carry output. The circuit works as follows:

1. When A and B are both low (0), the EX-OR gate produces a low output (0), and the AND gate also produces a low output (0). Therefore, the Sum output is low (0), and the Carry output is also low (0).

2. When A is high (1) and B is low (0), the EX-OR gate produces a high output (1), and the AND gate produces a low output (0). Therefore, the Sum output is high (1), and the Carry output is low (0).

3. When A is low (0) and B is high (1), the EX-OR gate produces a high output (1), and the AND gate produces a low