# 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).

NOT
AND
NAND
OR
NOR
XOR
XNOR
All Truth Tables
NOT

The simplest gate, this item inverts or reverses the signal. $Q= \overline A$

 Input (A) Output (Q) 0 1 1 0

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
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
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
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
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
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
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:

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.

There are tons of videos available about logic gates. If I had to pick a favourite, my current is this one, although she talks incredibly fast and you might need to slow it down or rewind.