> For the complete documentation index, see [llms.txt](https://cs.brash.ca/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://cs.brash.ca/unit-1/binary-and-logic/logic-gates.md).
# Logic Gates
Controlling electricity gives us the ability to make yes and no decisions or **`true`** and **`false`**. By combining two signals, we can give a single **`true`** or **`false`** answer, depending on the **`logic`**. The flow of electricity is controlled using **`gates`** (no, not named after Bill Gates - like a [gate](https://cdn.instructables.com/FT3/MIN3/IEOP6MV9/FT3MIN3IEOP6MV9.LARGE.jpg?auto=webp)).
{% tabs %}
{% tab title="NOT" %}
The simplest gate, this item **`inverts`** or reverses the signal. $$Q= \overline A$$
| Input (A) | Output (Q) |
| --------- | ---------- |
| 0 | 1 |
| 1 | 0 |
{% endtab %}
{% tab title="AND" %}
Only outputs true if both inputs are true. $$Q = A \cdot B \text{ or } A \times B$$
| A | B | Output (Q) |
| ------------ | - | ---------- |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
| {% endtab %} | | |
{% tab title="NAND" %}
Any gate with a dot is an `inverted` gate. $$Q = \overline{A \cdot B} \text{ or } \overline{A \times B}$$ \
This is the NOT AND gate:
| A | B | Output (Q) |
| ------------ | - | ---------- |
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
| {% endtab %} | | |
{% tab title="OR" %}
One or the other or both! $$Q = A+B$$
| A | B | Output (Q) |
| ------------ | - | ---------- |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
| {% endtab %} | | |
{% tab title="NOR" %}
Very simply NOT OR. $$Q = \overline{A+B}$$
| A | B | Output (Q) |
| ------------ | - | ---------- |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
| {% endtab %} | | |
{% tab title="XOR" %}
Exclusive OR meaning only one is true, not both. $$Q = A \bigoplus B$$
| A | B | Output (Q) |
| ------------ | - | ---------- |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
| {% endtab %} | | |
{% tab title="XNOR" %}
Exclusively NOT OR. If both inputs are the same, output true. $$Q = \overline{A \bigoplus B}$$
| A | B | Output (Q) |
| ------------ | - | ---------- |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
| {% endtab %} | | |
{% tab title="All Truth Tables" %}
| A | B | AND | NAND | OR | NOR | XOR | XNOR |
| - | - | --- | ---- | -- | --- | --- | ---- |
| 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 |
#### Individually:
{% endtab %}
{% endtabs %}
{% hint style="info" %}
The two "universal" gates are **`NOR`** and **`NAND`** - it is said that you can create all the other logic gates with a combination of just these two.
{% endhint %}
There are [tons of videos](https://www.youtube.com/results?search_query=logic+gates) available about logic gates. If I had to pick a favourite, my current is [this one](https://youtu.be/gI-qXk7XojA), although she talks incredibly fast and you might need to slow it down or rewind.
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