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).

Standard Logic Gate Symbols

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.