> For the complete documentation index, see [llms.txt](https://kevinli.gitbook.io/crafting-computer/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://kevinli.gitbook.io/crafting-computer/logic-circuits/and-gate.md).

# And Gate

The `not` gate we implemented just now is very simple, let's now check out a more complex circuit - the `and` gate.

We start by specifying the interface of the `and` gate.

Looking at the truth table of `and`, we notice that it expects two inputs `a` and `b` and produces a single output.

| a | b | a and b |
| - | - | ------- |
| 0 | 0 | 0       |
| 0 | 1 | 0       |
| 1 | 0 | 0       |
| 1 | 1 | 1       |

So we can declare the header of the `and` gate as:

```
and a[1] b[1] -> [1]
```

Great!

Now since `a and b` is equivalent to `not (a nand b)`, we can implement the body of the `and` gate as:

```
not (nand a b)
```

Combining the header and the body, we got:

```
and a[1] b[1] -> [1] =
    not (nand a b)
```